Trigonometry Table 0 To 360
Contents
- 0.1 What are the trig values from 0 to 360?
- 0.2 What is the trigonometry formula for 360 degrees?
- 0.3 How is sin360 0?
- 1 Is Sin 360 or 180?
- 2 What is tan in 360?
- 3 Where sin is 0?
- 4 What angle is zero?
- 5 What sin is zero?
- 6 What is value of cos 270?
- 7 Is Cos 120 negative?
- 8 What is the trick for trig values?
- 9 What is the 360 unit circle?
What are the trig values from 0 to 360?
Trigonometry Table- Trigonometric Values – Trigonometry table showing the values of common trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for angles in degrees:
| Degrees (°) | Sine (sin) | Cosine (cos) | Tangent (tan) | Cosecant (csc) | Secant (sec) | Cotangent (cot) |
|---|---|---|---|---|---|---|
| 0° | 1 | undefined | 1 | undefined | ||
| 30° | 1/2 | √3/2 | √3/3 | 2√3/3 | 2 | √3 |
| 45° | √2/2 | √2/2 | 1 | √2 | √2 | 1 |
| 60° | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
| 90° | 1 | undefined | 1 | undefined | ||
| 120° | √3/2 | -1/2 | -√3 | -2/√3 | -2 | -1/√3 |
| 135° | √2/2 | -√2/2 | -1 | -√2 | -√2 | -1 |
| 150° | 1/2 | -√3/2 | -√3/3 | -2√3/3 | -2 | -√3 |
| 180° | -1 | undefined | -1 | undefined | ||
| 210° | -1/2 | -√3/2 | √3/3 | -2√3/3 | -2 | √3 |
| 225° | -√2/2 | -√2/2 | 1 | -√2 | -√2 | 1 |
| 240° | -√3/2 | -1/2 | √3 | -2/√3 | -2 | 1/√3 |
| 270° | -1 | undefined | -1 | undefined | ||
| 300° | -√3/2 | 1/2 | -√3 | 2/√3 | 2 | -1/√3 |
| 315° | -√2/2 | √2/2 | -1 | √2 | √2 | -1 |
| 330° | -1/2 | √3/2 | -√3/3 | 2√3/3 | 2 | √3 |
| 360° | 1 | undefined | 1 | undefined |
Note: In this table, “undefined” indicates that the trigonometry formula is not defined for that particular angle. Also, the values shown are rounded to several decimal places for simplicity.
What is the trigonometry formula for 360 degrees?
What is the Value of Cos 360 Degrees in Terms of Cot 360°? – We can represent the cosine function in terms of the cotangent function using trig identities, cos 360° can be written as cot 360°/√(1 + cot²(360°)).
How is sin360 0?
The value of sin 360 degrees can be calculated by constructing an angle of 360° with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of sin 360° is equal to the y-coordinate (0). ∴ sin 360° = 0.
Is 0 undefined in trig?
Determine Which Values of Trigonometric Functions are Undefined – Trigonometry For which values of, where in the unit circle, is undefined? Possible Answers: Correct answer: Explanation : Recall that, Since the ratio of any two real numbers is undefined when the denominator is equal to, must be undefined for those values of where, Restricting our attention to those values of between and, when or, Hence, is undefined when or,
What is the domain of f(x) = sin x? Possible Answers: All positive numbers and 0 All negative numbers and 0 All real numbers except 0 Correct answer: All real numbers Explanation : The domain of a function is the range of all possible inputs, or x-values, that yield a real value for f(x). Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
Sine is defined as the ratio between the side length opposite to the angle in question and the hypotenuse (SOH, or sin x = opposite/hypotenuse). In any triangle created by the angle x and the x-axis, the hypotenuse is a nonzero number. As a result, the denominator of the fraction created by the definition sin x = opposite/hypotenuse is not equal to zero for any angle value x.
- Therefore, the domain of f(x) = sin x is all real numbers.
- What is the domain of f(x) = cos x? Possible Answers: All positive numbers and 0 All real numbers except 0 All negative numbers and 0 Correct answer: All real numbers Explanation : The domain of a function is the range of all possible inputs, or x-values, that yield a real value for f(x).
Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
- Cosine is defined as the ratio between the side length opposite to the angle in question and the hypotenuse (CAH, or cos x = adjacent/hypotenuse).
- In any triangle created by the angle x and the x-axis, the hypotenuse is a nonzero number.
- As a result, the denominator of the fraction created by the definition cos x = adjacent/hypotenuse is not equal to zero for any angle value x.
Therefore, the domain of f(x) = cos x is all real numbers. Which of the following trigonometric functions is undefined? Possible Answers: Correct answer: Explanation : Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
Secant is the reciprocal of cosine, so the secant of any angle x for which cos x = 0 must be undefined, since it would have a denominator equal to 0. The value of cos (pi/2) is 0, so the secant of (pi)/2 must be undefined. Which of the following trigonometric functions is undefined? Possible Answers: Correct answer: Explanation : Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
Cotangent is the reciprocal of tangent, so the cotangent of any angle x for which tan x = 0 must be undefined, since it would have a denominator equal to 0. The value of tan (pi) is 0, so the cotangent of (pi) must be undefined. Which of the following trigonometric functions is undefined? Possible Answers: Correct answer: Explanation : Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
Secant is the reciprocal of cosine, so the secant of any angle x for which cos x = 0 must be undefined, since it would have a denominator equal to 0. The value of cos 3(pi/2) is 0, so the secant of 3(pi)/2 must be undefined. Which of the following trigonometric functions is undefined? Possible Answers: Correct answer: Explanation : Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
Cotangent is the reciprocal of tangent, so the cotangent of any angle x for which tan x = 0 must be undefined, since it would have a denominator equal to 0. The value of tan (0) is 0, so the cotangent of (0) must be undefined. Which of the following trigonometric functions is undefined? Possible Answers: Correct answer: Explanation : Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
Cosecant is the reciprocal of sine, so the cosecant of any angle x for which sin x = 0 must be undefined, since it would have a denominator equal to 0. The value of sin (0) is 0, so the cosecant of 0 must be undefined. Which of the following trigonometric functions is undefined? Possible Answers: Correct answer: Explanation : Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
Tangent is defined as the ratio between the side length opposite to the angle in question and the side length adjacent to it (TOA, or tan x = opposite/adjacent). In a triangle created by the angle x and the x-axis, the adjacent side length lies along the x-axis; however, when the angle x lies on the y-axis, no length can be drawn along the x-axis to represent the angle.
As a result, the denominator of the fraction created by the definition tan x = opposite/adjacent is equal to zero for any angle along the y-axis (90 or 270 degrees, or pi/2 or 3pi/2 in radians.) Therefore, tan 3(pi)/2 is undefined. Which of the following trigonometric functions is undefined? Possible Answers: Correct answer: Explanation : Trigonometric functions are equal to 0, 1, -1 or undefined when the angle lies on an axis, meaning that the angle is equal to 0, 90, 180 or 270 degrees (0, (pi)/2, pi or 3(pi)/2 in radians.) Trigonometric functions are undefined when they represent fractions with denominators equal to zero.
Cosecant is the reciprocal of sine, so the cosecant of any angle x for which sin x = 0 must be undefined, since it would have a denominator equal to 0. The value of sin (pi) is 0, so the cosecant of pi must be undefined. Erik Certified Tutor University of Illinois at Urbana-Champaign, Bachelor of Science, Physics.
University of California-San Diego, Master of Scien. Kaitlyn Certified Tutor Fairfield University, Bachelor of Science, Biology, General. NUI Galway Ireland, Master of Science, Neuroscience. Abhisek Certified Tutor University of Florida, Bachelor of Engineering, Computer Science. If you’ve found an issue with this question, please let us know.
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Is Sin 360 or 180?
| θ | sin θ | cos θ |
|---|---|---|
| 90° | 1 | |
| 180° | −1 | |
| 270° | −1 | |
| 360° | 0 | 1 |
Why is cos 360 1?
Cos 360 Value –
- If we have to write cosine 360° value in radians, then we need to multiply 360° by π/180.
- Hence, cos 360° = cos (360 * π/180) = cos 2π
- So, we can write, cos 2π = 1
Here, π is denoted for 180°, which is half of the rotation of a unit circle. Hence, 2π denotes full rotation. So, for any number of a full rotation, n, the value of cos will remain equal to 1. Thus, cos 2nπ = 1. Moreover, we know that cos (-(-θ)) = cos(θ); therefore, even if we travel in the opposite direction, the value of cos 2nπ will always be equal. 
What is tan in 360?
The value of tan 360 degrees is 0, Tan 360 degrees in radians is written as tan (360° × π/180°), i.e., tan (2π) or tan (6.283185.,). In this article, we will discuss the methods to find the value of tan 360 degrees with examples.
Tan 360°: 0 Tan (-360 degrees): 0 Tan 360° in radians: tan (2π) or tan (6.2831853,,)
Where sin is 0?
The sine of 0 degrees is 0. In case of an angle of 0 degrees, the opposite side and the hypotenuse have the same length, which means that the sin 0 degrees is 0.
What angle is zero?
What is a Zero Angle? – An angle that does not form a vertex or measure 0 degrees is called a zero angle. It is also called zero radians. A zero angle is formed when both the rays or arms of the angle are pointing towards the same direction and vertex as just a point without any space. zero angle
What sin is zero?
Sine Definition In Terms of Sin 0
| Sine Degrees/Radians | Values |
|---|---|
| Sin 0 0 | 0 |
| Sin 30 0 or Sin π/6 | 1/2 |
| Sin 45 0 or Sin π/4 | 1 / 2 |
| Sin 60 0 or Sin π/3 | 3 / 2 |
What is value of sin 270?
Answer: Sin 270 degrees has a value of -1.
What is value of cos 270?
The value of cos 270 degrees is 0. Cos 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238.)
Why is sin 90 1?
Why does sin 90 degrees equal 1? We know that the formula of sin is pe. So if you want to know what sin(90 degrees) is check the y- coordinate when the angle is 90, well since the radius of the circle is 1, this implies that sin90 is 1. So you don’t really have to prove that sin 90 is 1, it is actually defined like that! Why does sin 90 degrees equal 1? We know that the formula of sin is pe.
- Introduction: In trigonometry, the sine function (sin) relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the hypotenuse.
- The value of sin 90 degrees is indeed 1, but it requires a deeper understanding of trigonometry to explain why.
- Understanding the Sine Function: The sine function is defined as the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse.
This definition holds true for any angle between 0 and 90 degrees. As the angle increases, the side opposite the angle also increases. The Right Triangle: To understand why sin 90 degrees equals 1, let’s consider a right triangle with one angle measuring 90 degrees.
- In this triangle, the side opposite the 90-degree angle is the longest side, known as the hypotenuse.
- The other two sides are the adjacent side and the opposite side.
- Explaining sin 90 degrees: When the angle is 90 degrees, the side opposite the angle is equal to the length of the hypotenuse.
- Mathematically, sin 90 degrees = opposite/hypotenuse.
Substituting the values, sin 90 degrees = hypotenuse/hypotenuse = 1. Visual Explanation: Visually, when the angle is 90 degrees, the opposite side aligns perfectly with the hypotenuse, forming a straight line. Since the length of the opposite side is equal to the length of the hypotenuse, the ratio of the opposite side to the hypotenuse is 1.
- Conclusion: In conclusion, sin 90 degrees equals 1 because, in a right triangle with a 90-degree angle, the side opposite the angle is equal to the length of the hypotenuse.
- The sine function represents the ratio of the opposite side to the hypotenuse, and when the two sides are equal, the ratio is 1.
Why does sin 90 degrees equal 1? We know that the formula of sin is pe. Sine, Cosine Tangent etc are defined ratios of base, height and hypoteneous of the a right angled triangle. that means one angle of triangle is already 90 degree. if another angle approaches 90 degree then base of the triangle approaches zero.
Is Cos 120 negative?
Cos 120° in Terms of Trigonometric Functions – Using trigonometry formulas, we can represent the cos 120 degrees as:
± √(1-sin²(120°)) ± 1/√(1 + tan²(120°)) ± cot 120°/√(1 + cot²(120°)) ±√(cosec²(120°) – 1)/cosec 120° 1/sec 120°
Note: Since 120° lies in the 2nd Quadrant, the final value of cos 120° will be negative. We can use trigonometric identities to represent cos 120° as,
-cos(180° – 120°) = -cos 60° -cos(180° + 120°) = -cos 300° sin(90° + 120°) = sin 210° sin(90° – 120°) = sin(-30°)
☛ Also Check:
cos 210 degrees cos 90 degrees cos 225 degrees cos 540 degrees cos 58 degrees cos 1170 degrees
What is value of cos 150?
What is the Value of Cos 150 Degrees? – The value of cos 150 degrees in decimal is -0.866025403. Cos 150 degrees can also be expressed using the equivalent of the given angle (150 degrees) in radians (2.61799,,) We know, using degree to radian conversion, θ in radians = θ in degrees × ( pi /180°) ⇒ 150 degrees = 150° × (π/180°) rad = 5π/6 or 2.6179, 
Explanation: For cos 150 degrees, the angle 150° lies between 90° and 180° (Second Quadrant ). Since cosine function is negative in the second quadrant, thus cos 150° value = −√3/2 or -0.8660254. Since the cosine function is a periodic function, we can represent cos 150° as, cos 150 degrees = cos(150° + n × 360°), n ∈ Z.
What is sin 160 equal to?
Here, the value of sin 160° is equal to 0.342.
What is sin infinity?
H1: What is the value of sin and cos infinity? – Mathematics – Answer: The trigonometric ratios refer to the ratios of length of the sides of a right-angled triangle to its respective angle. These trigonometric ratios are named as follows: sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosec and sec. Let us consider a right-angled triangle to understand these ratios. 
Therefore
Sinθ= Perpendicular/Hypotenuse Cosθ= Base/Hypotenuse Tanθ= Perpendicular/Base Secθ= Hypotenuse/Base Cosecθ= Hypotenuse/Perpendicular Cotθ= Base/Perpendicular
Hence for different angles i.e at 0, 30, 45, 60, 90 and infinity, the value of these ratios is different. The following table shows the values of these ratios at different angles.
| Angle | 0° | 30° | 45° | 60° | 90° |
| Sin | 0 | 1/2 | 1/√2 | 3/2 | 1 |
| Cos | 1 | 3/2 | 1/√2 | 1/2 | 0 |
| Tan | 0 | 1/3 | 1 | 3 | Not Defined |
Hence, to find the value of sin and cos infinity, we have to follow the following steps: It is known to us that, (-1) ≤ sin x, cos x ≤ (+1) for x ε (- α, +α) i.e., sin x and cos x values generally lie in between – 1 to 1. Likewise, ∞ is not defined along these lines, sin (∞) and cos (∞) can’t have exact values.
Is dividing by zero infinity?
something/0 : – You might be wondering after seeing these answers. If you are not, it is good. The thing is something divided by 0 is always undefined because the value has not been defined yet. So, when do we say this something divided by 0 is infinity? Of course, we have seen these a lot of time but why do we say this? Well, something divided by 0 is infinity is the only case when we use limit.
Why can’t we divide by 0?
As much as we would like to have an answer for ‘what’s 1 divided by 0?’ it’s sadly impossible to have an answer. The reason, in short, is that whatever we may answer, we will then have to agree that that answer times 0 equals to 1, and that cannot be true, because anything times 0 is 0.
What is the value of the cosec 360 0 ɵ equal to?
The value of cosec 360° is equal to the reciprocal of the y-coordinate (0). ∴ cosec 360° = undefined(∞).
What is cot 360 value in trigonometry?
Cot 360 degrees is the value of cotangent trigonometric function for an angle equal to 360 degrees. The value of cot 360° is undefined(∞).
What is the trick for trig values?
So there we have a really easy way of remembering those exact values we use our hand the special angle 0 30 45 60 and 90. and just remember for sine and cos it’s root fingers divided by two sine is root fingers below the bent finger. and cos is root finger above the bent finger.
What is the 360 unit circle?
Negative angles – \r\nJust when you thought that angles measuring up to 360 degrees or 2π radians was enough for anyone, you’re confronted with the reality that many of the basic angles have negative values and even multiples of themselves. If you measure angles clockwise instead of counterclockwise, then the angles have negative measures:\r\n\r\nA 30-degree angle is the same as an angle measuring –330 degrees, because they have the same terminal side. \r\n\r\nis the same as an angle of\r\n\r\n \r\n\r\nBut wait — you have even more ways to name an angle. By doing a complete rotation of two (or more) and adding or subtracting 360 degrees or a multiple of it before settling on the angle’s terminal side, you can get an infinite number of angle measures, both positive and negative, for the same basic angle.\r\n\r\nFor example, an angle of 60 degrees has the same terminal side as that of a 420-degree angle and a –300-degree angle. \r\n\r\nAlthough this name-calling of angles may seem pointless at first, there’s more to it than arbitrarily using negatives or multiples of angles just to be difficult. The angles that are related to one another have trig functions that are also related, if not the same.”,”blurb”:””,”authors”:,”primaryCategoryTaxonomy”: },”secondaryCategoryTaxonomy”:,”tertiaryCategoryTaxonomy”:,”trendingArticles”:null,”inThisArticle”:,”relatedArticles”: }, }, }, }, }],”fromCategory”:},”hasRelatedBookFromSearch”:false,”relatedBook”:,”image”:,”title”:”Trigonometry For Dummies”,”testBankPinActivationLink”:””,”bookOutOfPrint”:false,”authorsInfo”:” Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others. “,”authors”:,”_links”: },”collections”:,”articleAds”:, ]\” id=\”du-slot-63221aef143db\”> “,”rightAd”:” “},”articleType”: },”sponsorship”:,”brandingLine”:””,”brandingLink”:””,”brandingLogo”:,”sponsorAd”:””,”sponsorEbookTitle”:””,”sponsorEbookLink”:””,”sponsorEbookImage”: },”primaryLearningPath”:”Advance”,”lifeExpectancy”:”Five years”,”lifeExpectancySetFrom”:”2021-07-07T00:00:00+00:00″,”dummiesForKids”:”no”,”sponsoredContent”:”no”,”adInfo”:””,”adPairKey”:},”status”:”publish”,”visibility”:”public”,”articleId”:149216},”articleLoadedStatus”:”success”},”listState”:,”objectTitle”:””,”status”:”initial”,”pageType”:null,”objectId”:null,”page”:1,”sortField”:”time”,”sortOrder”:1,”categoriesIds”:,”articleTypes”:,”filterData”:,”filterDataLoadedStatus”:”initial”,”pageSize”:10},”adsState”:,”adsId”:0,”data”:, );(function() )(); \r\n”,”enabled”:true}, return null};\r\nthis.set=function(a,c) ;\r\nthis.check=function() return!0};\r\nthis.go=function() };\r\nthis.start=function(),!1):window.attachEvent&&window.attachEvent(\”onload\”,function() ):t.go()};};\r\ntry catch(i) })();\r\n \r\n”,”enabled”:false}, ;\r\n h._hjSettings= ;\r\n a=o.getElementsByTagName(‘head’);\r\n r=o.createElement(‘script’);r.async=1;\r\n r.src=t+h._hjSettings.hjid+j+h._hjSettings.hjsv;\r\n a.appendChild(r);\r\n })(window,document,’https://static.hotjar.com/c/hotjar-‘,’.js?sv=’);\r\n “,”enabled”:false},,, ]}},”pageScriptsLoadedStatus”:”success”},”navigationState”:,,,,,,,,, ],”navigationCollectionsLoadedStatus”:”success”,”navigationCategories”:,,,, ],”breadcrumbs”:,”categoryTitle”:”Level 0 Category”,”mainCategoryUrl”:”/category/books/level-0-category-0″}},”articles”:,,,, ],”breadcrumbs”:,”categoryTitle”:”Level 0 Category”,”mainCategoryUrl”:”/category/articles/level-0-category-0″}}},”navigationCategoriesLoadedStatus”:”success”},”searchState”:,”routeState”:,”params”:,”fullPath”:”/article/academics-the-arts/math/trigonometry/positive-and-negative-angles-on-a-unit-circle-149216/”,”meta”:,”prerenderWithAsyncData”:true},”from”:,”params”:,”fullPath”:”/”,”meta”: }},”dropsState”:,”sfmcState”:,”profileState”:,”userOptions”:,”status”:”success”}} The unit circle is a platform for describing all the possible angle measures from 0 to 360 degrees, all the negatives of those angles, plus all the multiples of the positive and negative angles from negative infinity to positive infinity.
