## Sin Cos Tan Table #### What is the formula of cos sin tan?

Sin Cos Tan Formula – The three ratios, i.e. sine, cosine and tangent have their individual formulas. Suppose, ABC is a right triangle, right-angled at B, as shown in the figure below: Now as per sine, cosine and tangent formulas, we have here:

• Sine θ = Opposite side/Hypotenuse = BC/AC
• Cos θ = Adjacent side/Hypotenuse = AB/AC
• Tan θ = Opposite side/Adjacent side = BC/AB
• We can see clearly from the above formulas, that:
• Tan θ = sin θ/cos θ
• Now, the formulas for other trigonometry ratios are:
• Cot θ = 1/tan θ = Adjacent side/ Side opposite = AB/BC
• Sec θ = 1/Cos θ = Hypotenuse / Adjacent side = AC / AB
• Cosec θ = 1/Sin θ = Hypotenuse / Side opposite = AC / BC

The other side of representation of trigonometric values formulas are:

• Tan θ = sin θ/cos θ
• Cot θ = cos θ/sin θ
• Sin θ = tan θ/sec θ
• Cos θ = sin θ/tan θ
• Sec θ = tan θ/sin θ
• Cosec θ = sec θ/tan θ

#### How to solve trigonometric tables?

Download Article Memorization tips and tricks to make calculating sine, cosine, and tangent a breeze Download Article Trigonometry (or trig) is one of the most fun branches of math, but it’s tough remembering all the key numbers and formulas. If you’re struggling with trig, you’ve come to the right place. We’re here to help you remember all kinds of trigonometric equations with easy-to-follow methods.

Angles (in Degrees) 30° 45° 60° 90°
sin𝛳 0 1 / 2 √2 / 2 √3 / 2 1
cos𝛳 1 √3 / 2 √2 / 2 1 / 2 0
tan𝛳 0 √3 / 3 1 √3 Not defined
cosec𝛳 Not defined 2 √2 2√3 / 3 1
sec𝛳 1 2√3 / 3 √2 2 Not defined
cotan𝛳 Not defined √3 1 √3 / 3 0

table>

Angles (in Degrees) 0° 30° 45° 60° 90° sin𝛳 0 0.5 0.707 0.866 1 cos𝛳 1 0.866 0.707 0.5 0 tan𝛳 0 0.577 1 1.732 Not defined cosec𝛳 Not defined 2 1.414 1.155 1 sec𝛳 1 1.155 1.414 2 Not defined cotan𝛳 Not defined 1.732 1 0.577 0

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• 1 Draw a blank trigonometry table. Creating a trigonometric table can help you remember key trig formulas. Design your table to have 6 rows and 6 columns. In the 1st column, write down the key trigonometric ratios (sine, cosine, tangent, cosecant, secant, and cotangent). In the 1st row, write down the angles you’ll most commonly be using in trigonometry (0°, 30°, 45°, 60°, 90°).

Sine, cosine, and tangent are the more commonly used trigonometric ratios, although you should also learn cosecant, secant, and cotangent to have a more in-depth knowledge of trigonometry and the trigonometric table.

• 2 Number your table’s columns in ascending order, starting at 0. Once you’ve created your 6 rows and columns, assign each column a number from 0-4. The number for the 0° column should be 0, the number for 30° should be 1, 45° should be 2, 60° should be 3, and 90° should be 4. Advertisement
• 3 Use √x/2 to find the values for your table’s sine row. Plug in each column’s number into the formula √x/2. Use this formula to calculate the sine values for 0°, 30°, 45°, 60°, and 90° and write those values in your table.
• For example, for the first entry in the sine column (sin 0°), set x to equal 0 and plug it into the expression √x/2. This will give you √0/2, which can be simplified to 0/2 and then finally to 0.
• Plugging the angles into the expression √x/2 in this way, the remaining entries in the sine row are √1/2 (which can be simplified to ½, since the square root of 1 is 1), √2/2 (which can be simplified to 1/√2, since √2/2 is also equal to (1 x √2)/(√2 x √2) and in this fraction, the “√2” in the numerator and a “√2” in the denominator cancel each other out, leaving 1/√2), √3/2, and √4/2 (which can be simplified to 1, since the square root of 4 is 2 and 2/2 = 1).
• Once the sine row is filled, it’ll be a lot easier to fill in the remaining rows.
• 4 Place the sine row entries in the cosine row in reverse order. Mathematically speaking, sin x° = cos (90-x)° for any x value. Thus, to fill in the cosine row, simply take the entries in the sine row and place them in reverse order in the cosine row. Fill in the cosine row so that the value for the sine of 90° is also used as the value for the cosine of 0°, the value for the sine of 60° is used as the value for the cosine of 30°, and so on.
• For example, since 1 is the value placed in the final entry in the sine column (sine of 90°), this value will be placed in the 1st entry for the cosine column (cosine of 0°).
• Once filled, the values in the cosine row should be 1, √3/2, 1/√2, ½, and 0.
• 5 Divide your sine values by the cosine values to fill the tangent row. Simply speaking, tangent = sine/cosine. Therefore, for every angle, take its sine value and divide it by its cosine value to calculate the corresponding tangent value.
• To take 30° as an example: tan 30° = sin 30° / cos 30° = (√1/2) / (√3/2) = 1/√3.
• The entries of your tangent row should be 0, 1/√3, 1, √3, and undefined for 90°. The tangent of 90° is undefined because sin 90° / cos 90° = 1/0 and division by 0 is always undefined.
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• 6 Reverse the entries in the sine row to find the cosecant of an angle. Starting from the bottom row (or denominator) of the sine row, take the sine values you’ve already calculated and place them in reverse order (above the numerator) in the cosecant row. This works because the cosecant of an angle is equal to the inverse of the sine of that angle.

For instance, use the sine of 90° to fill in the entry for the cosecant of 0°, the sine of 60° for the cosecant of 30°, and so on.

• 7 Reverse the entries of the cosine row to fill out the secant row. Starting from the cosine of 90°, enter the values from the cosine row in the secant row, such that value for the cosine of 90° is used as the value for the secant of 0°, the value for the cosine of 60° is used as the value for the secant of 30°, and so on.

This is mathematically valid because the inverse of the cosine of an angle is equal to that angle’s secant.

• 8 Fill the cotangent row by reversing the values from the tangent row. Take the value for the tangent of 90° and place it in the entry space for the cotangent of 0° in your cotangent row. Do the same for the tangent of 60° and the cotangent of 30°, the tangent of 45° and the cotangent of 45°, and so on, until you’ve filled in the cotangent row by inverting the order of entries in the tangent row.
• This works because the cotangent of an angle is equal to the inversion of the tangent of an angle.
• You can also find the cotangent of an angle by dividing its cosine by its sine.

1. 1 Draw a right triangle around the angle you’re working with. For an easy way to memorize the formulas of trigonometric ratios, start by extending 2 straight lines out from the sides of the angle. Then, draw a third line perpendicular to 1 of these 2 lines to create a right angle.
• If you’re calculating sine, cosine, or tangent in the context of a math class, it’s likely you’ll already be working with a right triangle.
• Right triangles are a key part of remembering right-angled trigonometry and trig in general.
2. 2 Calculate sine, cosine, or tangent by using the sides of the triangle. The sides of the triangle can be identified in relation to the angle as the “opposite” (the side opposite of the angle), the “adjacent” (the side next to the angle other than the hypotenuse), and the “hypotenuse” (the side opposite the right angle of the triangle).
• The sine of an angle is equal to the opposite side divided by the hypotenuse.
• The cosine of an angle is equal to the adjacent side divided by the hypotenuse.
• The tangent of an angle is equal to the opposite side divided by the adjacent side.
• For example, to determine the sine of a 35° angle, divide the length of the opposite side of the triangle by the hypotenuse. If the opposite side’s length was 2.8 and the hypotenuse was 4.9, then the sine of the angle would be 2.8/4.9, which is equal to 0.57.
3. 3 Use a mnemonic device to remember ratios for sin, cos, and tan. The most commonly used acronym to remember trigonometric ratios is SOHCAHTOA, which stands for “Sine Opposite Hypotenuse, Cosine Adjacent Hypotenuse, Tangent Opposite Adjacent.” To better remember this acronym, spell out a mnemonic phrase with these letters like “She Offered Her Child A Heaping Teaspoon Of Applesauce.”
4. 4 Inverse the sine, cosine, or tangent to find their reciprocal ratios. To calculate cosecant, secant, and cotangent, simply invert the ratios of each triangle side using SOHCAHTOA. Because cosecant is the inverse of sine, it is equal to the hypotenuse divided by the opposite side.
• For example, if you wanted to find the cosecant of a 35°, with an opposite side length of 2.8 and a hypotenuse of 4.9, you would divide 4.9 by 2.8 to get a cosecant of 1.75.

• Question How do I write sec and co-sec values? Values of cosec, sec and cot can be found by taking inverse of sin, cos and tan respectively for the given angle.
• Question Why tan 90 degree is not defined? The sine of 90° equals 1, and the cosine of 90° equals zero. It happens that the tangent of any angle is equal to its sine divided by its cosine. Thus, the tangent of 90° equals 1 divided by zero. However, dividing by zero is “undefined,” because it equals infinity (which is not a defined number). That makes the tangent of 90° undefined.
• Question How do I fill a cosec and sec value? You can reverse the numerator and denominator of sin to find cosec like (30°= 0= 1/0 i.e., not defined) and of cos to find sec.

Avoid leaving irrational numbers in the denominator. For example, tan30° = 1/√3. Don’t leave it that way. Instead, simplify the expression by multiplying the fraction by √3/√3 (which is equal to 1 and thus doesn’t change the value of the original expression), which is equal to (1 x √3)/(√3 x √3), which simplifies to √3/3.

Because you can’t divide by 0, you can’t reach a definable answer for tan 90° or cot 0°. Write “not defined” or “n/a” (not applicable) instead.

Advertisement Article Summary X To remember the trigonometric table, use the acronym “SOHCAHTOA,” which stands for “Sine opposite hypotenuse, cosine adjacent hypotenuse, tangent opposite adjacent. For example, if you wanted to calculate the sine of an angle or triangle, you’d know that sine is “sine opposite hypotenuse” based on “SOHCAHTOA.” Therefore, you would just divide the opposite side of the triangle by the hypotenuse to get the sine.

#### What is 0 30 45 60 90 trigonometry?

Important Angles of Trigonometry – The special angles used in trigonometry are 0°, 30°, 45°, 60° and 90°. These are the common angles which are used while performing computations of trigonometric problems. Hence, it is suggested for students to memorise the values of trigonometric ratios (sine, cosine and tangent) for these angles, to do quick calculations.

## What is value of sin 45?

What is Sin 45 Degrees? Sin 45 degrees is the value of sine trigonometric function for an angle equal to 45 degrees. The value of sin 45° is 1/√2 or 0.7071 (approx).

## Is sin 120 equal to sin 60?

How to Derive the Value of Sin 120 Degrees? – By using the unit circle, the value of sin 120 can be calculated. We know the radius of the circle is the hypotenuse of the right triangle which is equal to the value 1. From the cartesian plane, we take, x= cos and y = sin By looking at the diagram given above, the value of sin 60 is equal to the value of sin 120. It means that, sin 60 = sin 120 = √3/2.

### What is the trigonometric rule formula?

What is the Basic Trigonometry Formula? – Basic trigonometry formulas involve the representing of basic trigonometric ratios in terms of the ratio of corresponding sides of a right-angled triangle. These are given as, sin θ = Opposite Side/ Hypotenuse, cos θ = Adjacent Side/Hypotenuse, tan θ = Opposite Side/Adjacent Side.

### Can you solve trig without calculator?

Evaluating Trigonometric Functions without a Calculator For trigonometric functions of Graphical Axes, you can easily solve the problems using the easy-to-remember patterns for 0°, 90°, 180°, and 270°. The values of Sine and Cosine for these angles are quite easy to be saved in your memory.

## How is cos 180 =- 1?

How to obtain the value of Cos 180°? – The value of cos 180 degrees, or cos pi, may be expressed in terms of several angles such as 0°, 90°, and 270°. Consider the unit circle, which in the Cartesian plane is divided into four quadrants. The value of cos 180 degrees from the Cartesian plane is calculated using the value 180 degrees in the second quadrant,

Because the second quadrant’s cosine values are always negative. From the cos value equal to 0, we will derive the value of cos 180°. The exact value of cos 0 degrees is 1 as we know. As a result, the cos 180 degree is -(cos 0), which equals – (1) Hence, cos 180 degrees is equal to -1. Radians are also used to represent it.

So, the value of cos = -1, when the value of = 180. There are a few more ways for cosine derivation. To determine the value, several degree values of sine and cosine functions are obtained from the trigonometry table, As we know, 180° – 0° = 180° ——— (A) 270° – 90° = 180° ——— (B)

#### Why is tan180 0?

Tan 180° in Terms of Trigonometric Functions – Using trigonometry formulas, we can represent the tan 180 degrees as:

sin(180°)/cos(180°) ± sin 180°/√(1 – sin²(180°)) ± √(1 – cos²(180°))/cos 180° ± 1/√(cosec²(180°) – 1) ± √(sec²(180°) – 1) 1/cot 180°

Note: Since 180° lies on the negative x-axis, the final value of tan 180° is 0. We can use trigonometric identities to represent tan 180° as,

cot(90° – 180°) = cot(-90°) -cot(90° + 180°) = -cot 270° -tan (180° – 180°) = -tan 0°

## Is 120 a special angle?

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Page ID 18478 Angles such as 30°, 45°, 60°, 90°, or 120° are called special angles. They all divide evenly into 360°. We call nonspecial angles general angles, In the examples in Figure 10.43, and others considered previously, we started with rotation axes and mirror planes that intersected at special angles. Figure 10.44: Infinite symmetry is not possible The first diagram in Figure 10.44 shows two intersecting 2-fold axes and three points related by them. The angle between the axes is small and does not divide evenly into 360°. It is a general angle. We may apply the 2-fold axes to each other to generate more 2-fold axes and points, moving around the diagram in a stepwise manner as shown.

We could do this forever, continuing around the circle indefinitely, because the new axes and points we generate will never coincide with others already present. When we continue this operation all the way around the circle, we will not end back where we started. So, the number of 2-fold axes becomes infinite, and an infinite-fold axis of symmetry must be perpendicular to the plane of the page.

This is equivalent to the symmetry of a circle. Since crystals consist of a discrete number of faces (and atomic arrangements consist of a discrete number of atoms), we know that infinite symmetry is not possible. We may therefore conclude that if crystals have two 2-fold axes, they must intersect at a special angle so that they are finite in number. Figure 10.45: Possible intersection angles for rotation axes The preceding discussion suggests that rotation axes only combine in a limited number of ways. In fact, angles between rotation axes are limited to the seven depicted in Figure 10.45. We have already seen examples of each.

These drawings are of a cube and a hexagonal prism, but angles between rotation axes in crystals of other shapes are limited to the same seven values. The possible angles between rotation axes are all special angles. If we carried out the exercise, we would find that in crystals with both rotation axes and mirror planes, the angles between the rotation axes and the mirror planes are limited to only a few special angles as well.

Otherwise, we have infinite symmetry. In most crystals the angles are 0° (the rotation axis lies within the plane of the mirror) or 90° (the rotation axis is perpendicular to the mirror).

## What is 72 formula of trigonometry?

What is the Value of Cos 72 Degrees? – The value of cos 72 degrees in decimal is 0.309016994. Cos 72 degrees can also be expressed using the equivalent of the given angle (72 degrees) in radians (1.25663,,) We know, using degree to radian conversion, θ in radians = θ in degrees × ( pi /180°) ⇒ 72 degrees = 72° × (π/180°) rad = 2π/5 or 1.2566, Explanation: For cos 72 degrees, the angle 72° lies between 0° and 90° (First Quadrant ). Since cosine function is positive in the first quadrant, thus cos 72° value = (√5 – 1)/4 or 0.3090169. Since the cosine function is a periodic function, we can represent cos 72° as, cos 72 degrees = cos(72° + n × 360°), n ∈ Z.

#### How easy is trigonometry?

Trigonometry is hard for some students while others find it easy. Science students learn trigonometry at the school level, while complex or advanced trigonometry is taught in high school.

### Is trigonometry in class 12?

List of Class 12 Trigonometry Formulas – CBSE Class 12 mathematics contains Inverse Trigonometric Functions. This chapter includes definitions, graphs and elementary properties of inverse trigonometric functions. Trigonometry formulas for class 12 play a critical role in these chapters. Hence, all trigonometry formulas are provided here.

## When sin will be 1?

The function sin 1 is equal to the sine of the angle 90°, which is 1. As a result, the inverse function of sin 1 is 90° or /2. It is the sine function’s maximum value.

#### What angle is depression?

Angle of Depression Definition – The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object’s distance from the ground are known to us.

1. Its an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.
2. If the object observed by the observer is below the level of the observer, then the angle formed between the horizontal line and the observer’s line of sight is called the angle of depression.

In the below figure, θ is the angle of depression.

#### What is sin theta?

Trigonometric ratios – Trigonometric ratios are ratios of the lengths of the right-angled triangle. These ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle.

Sine function: The sine ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its opposite side to its hypotenuse.

i.e., Sinθ = AB/AC

Cosine function: The Cosine ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its adjacent side to its hypotenuse.

i.e, Cosθ = BC/AC

Tangent Function: The Tangent ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its opposite side to its adjacent.

i.e, Tanθ = AB/BC

Cotangent Function: The Cotangent ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its adjacent side to its opposite. It’s the reciprocal of the tan ratio.

i.e, Cotθ = BC/AB =1/Tanθ

Secant Function: The Secant ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its Hypotenuse side to its adjacent.

i.e, Secθ = AC/BC

Cosecant Function: The Cosecant ratio for the given angle θ in a right-angled triangle is defined as the ratio of lengths of its hypotenuse side to its opposite.

i.e, Cosecθ = AC/AB In a Right-angled triangle, the sine function or sine theta is defined as the ratio of the opposite side to the hypotenuse of the triangle. In a triangle, the Sine rule helps to relate the sides and angles of the triangle with its circumradius(R) i.e, a/SinA = b/SinB = c/SinC = 2R.

• From the above figure, sine θ can be written as
• Sinθ = AB / AC
• According to the Pythagoras theorem, we know that AB 2 + BC 2 = AC 2, On dividing both sides by AC 2
• ⇒ (AB/AC) 2 + (BC/AC) 2
• ⇒ Sin 2 θ + Cos 2 θ = 1

### What is the formula of trigonometry?

Basic Trigonometric Function Formulas – There are basically 6 ratios used for finding the elements in Trigonometry. They are called trigonometric functions. The six trigonometric functions are sine, cosine, secant, cosecant, tangent and cotangent. By using a right-angled triangle as a reference, the trigonometric functions and identities are derived:

• sin θ = Opposite Side/Hypotenuse
• cos θ = Adjacent Side/Hypotenuse
• tan θ = Opposite Side/Adjacent Side
• sec θ = Hypotenuse/Adjacent Side
• cosec θ = Hypotenuse/Opposite Side
• cot θ = Adjacent Side/Opposite Side

### What is tan a formula?

What Are Tangent Formulas? – The tangent formulas are related to the tangent function. The important tangent formulas are as follows:

tan x = (opposite side) / (adjacent side) tan x = 1 / (cot x) tan x = (sin x) / (cos x) tan x = ± √( sec 2 x – 1)

### What is the angle formula?

What are the Formulas to Find the Angles? – Angles Formulas at the center of a circle can be expressed as, Central angle, θ = (Arc length × 360º)/(2πr) degrees or Central angle, θ = Arc length/r radians, where r is the radius of the circle. Multiple angles in terms of trignometry:

Sin nθ =$$\sum_ ^ \;cos^ \theta \; sin^ \theta\; Sin\left \pi$$ Cos nθ =$$\sum_ ^ cos^ \theta \,sin^ \theta \;cos\left$$ Tan nθ= Sin nθ/ Cos nθ

## What’s the formula for cosine?

Right triangles and cosines – Consider a right triangle ABC with a right angle at C. As mentioned before, we’ll generally use the letter a to denote the side opposite angle A, the letter b to denote the side opposite angle B, and the letter c to denote the side opposite angle C.

Since the sum of the angles in a triangle equals 180°, and angle C is 90°, that means angles A and B add up to 90°, that is, they are complementary angles. Therefore the cosine of B equals the sine of A. We saw on the last page that sin A was the opposite side over the hypotenuse, that is, a/c. Hence, cos B equals a/c.

### ■ Easy trick to remember sin, cos and tan values!

In other words, the cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse: Also, cos A = sin B = b/c. 