## Trigonometry Table Class 10

Contents

## What is trigonometric tables class 10?

Trigonometry Table is a standard table that helps us to find the values of trigonometric ratios for standard angles such as 0°, 30°, 45°, 60°, and 90°. Trigonometric table comprises of all six trigonometric ratios: sine, cosine, tangent, cosecant, secant, cotangent.

## What is trigonometry class 10 maths?

CBSE Class 10 Maths Notes Chapter 8 Introduction to Trigonometry –

Position of a point P in the Cartesian plane with respect to co-ordinate axes is represented by the ordered pair (x, y). Trigonometry is the science of relationships between the sides and angles of a right-angled triangle. Trigonometric Ratios : Ratios of sides of right triangle are called trigonometric ratios. Consider triangle ABC right-angled at B. These ratios are always defined with respect to acute angle ‘A’ or angle ‘C. If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of an angle can be easily determined. How to identify sides: Identify the angle with respect to which the t-ratios have to be calculated. Sides are always labelled with respect to the ‘θ’ being considered.

Let us look at both cases: In a right triangle ABC, right-angled at B. Once we have identified the sides, we can define six t-Ratios with respect to the sides.

case I | case II |

(i) sine A = \(\frac =\frac \) | (i) sine C = \(\frac =\frac \) |

(ii) cosine A = \(\frac =\frac \) | (ii) cosine C = \(\frac =\frac \) |

(iii) tangent A = \(\frac =\frac \) | (iii) tangent C = \(\frac =\frac \) |

(iv) cosecant A = \(\frac =\frac \) | (iv) cosecant C = \(\frac =\frac \) |

(v) secant A = \(\frac =\frac \) | (v) secant C = \(\frac =\frac \) |

(v) cotangent A = \(\frac =\frac \) | (v) cotangent C = \(\frac =\frac \) |

Note from above six relationships: cosecant A = \(\frac \), secant A = \(\frac \), cotangent A = \(\frac \), However, it is very tedious to write full forms of t-ratios, therefore the abbreviated notations are: sine A is sin A cosine A is cos A tangent A is tan A cosecant A is cosec A secant A is sec A cotangent A is cot A TRIGONOMETRIC IDENTITIES An equation involving trigonometric ratio of angle(s) is called a trigonometric identity, if it is true for all values of the angles involved.

sin² θ + cos² θ = 1 ⇒ sin² θ = 1 – cos² θ ⇒ cos² θ = 1 – sin² θ cosec² θ – cot² θ = 1 ⇒ cosec² θ = 1 + cot² θ ⇒ cot² θ = cosec² θ – 1 sec² θ – tan² θ = 1 ⇒ sec² θ = 1 + tan² θ ⇒ tan² θ = sec² θ – 1 sin θ cosec θ = 1 ⇒ cos θ sec θ = 1 ⇒ tan θ cot θ = 1

ALERT: A t-ratio only depends upon the angle ‘θ’ and stays the same for same angle of different sized right triangles. Value of t-ratios of specified angles:

∠A | 0° | 30° | 45° | 60° | 90° |

sin A | \(\frac \) | \(\frac } \) | \(\frac } \) | 1 | |

cos A | 1 | \(\frac } \) | \(\frac } \) | \(\frac \) | |

tan A | \(\frac } \) | 1 | √3 | not defined | |

cosec A | not defined | 2 | √2 | \(\frac } \) | 1 |

sec A | 1 | \(\frac } \) | √2 | 2 | not defined |

cot A | not defined | √3 | 1 | \(\frac } \) |

The value of sin θ and cos θ can never exceed 1 (one) as opposite side is 1. Adjacent side can never be greater than hypotenuse since hypotenuse is the longest side in a right-angled ∆. ‘t-RATIOS’ OF COMPLEMENTARY ANGLES If ∆ABC is a right-angled triangle, right-angled at B, then ∠A + ∠C = 90° or ∠C = (90° – ∠A) Thus, ∠A and ∠C are known as complementary angles and are related by the following relationships: sin (90° -A) = cos A; cosec (90° – A) = sec A cos (90° – A) = sin A; sec (90° – A) = cosec A tan (90° – A) = cot A; cot (90° – A) = tan A

#### What is the trick for trigonometry?

Second Trick – Let&’s learn one hand trick to remember the trigonometric table easily! Set each finger at standard angles as shown in the picture. To fill in the sine values in the trigger table we’ll include the number of fingers, while for the cosine table we’ll just fill in the values in reverse order. Image Source: wikimedia.org

- Step 1: For the sine table, count the fingers on the left side at a standard angle.
- Step 2: In this step, Divide the number of fingers by 4
- Step 3: Find the square root of the ratio.

### Does tan 90 exist?

What is the exact value of tan 90? The exact value of tan 90 is infinity or undefined.

#### Is trigonometry easy?

In general, trigonometry is considered hard, especially when right triangle numerals are given as word problems. However, an exact answer to this question depends upon a number of factors as some people find trigonometry hard while others think it to be relatively easy.

### How do you find sin 37?

How to Find the Value of Sin 37 Degrees? – The value of sin 37 degrees can be calculated by constructing an angle of 37° with the x-axis, and then finding the coordinates of the corresponding point (0.7986, 0.6018) on the unit circle, The value of sin 37° is equal to the y-coordinate (0.6018). ∴ sin 37° = 0.6018.

## What are the 3 types of trigonometry?

Types of Trigonometry Updated April 25, 2017 By Brooke Ashley Trigonometry is a branch of mathematics that uses variables to determine heights and distances. There are four types of trigonometry used today, which include core, plane, spherical and analytic. ••• PhotoObjects.net/PhotoObjects.net/Getty Images This type of trigonometry is used for triangles that have one 90 degree angle. Mathematicians use sine and cosine variables within a formula (as well as data from trigonometry tables such as decimal values) to determine the height and distance of the other two angles. ••• Jupiterimages/Photos.com/Getty Images Plane trigonometry is used for determining the height and distances of the angles in a plane triangle. This type of triangle has three vertices (points of intersection) on the surface, and the sides of the triangle are straight lines. ••• Photos.com/AbleStock.com/Getty Images Spherical trigonometry deals with triangles that are drawn on a sphere, and this type is often used by astronomers and scientists to determine distances within the universe. Unlike core or plane trigonometry, the sum of all angles in a triangle is greater than 180 degrees. ••• Hemera Technologies/PhotoObjects.net/Getty Images A subtype of core trigonometry, analytic seeks to determine values based upon the x-y plane of a triangle. The sine (and cosine) of the sum of two angles is used to obtain the sine (and cosine) of a double angle.

## Is trigonometry grade 11?

Grade 11 Math Unit 6 – Trigonometric Functions (Ontario MCR3U) — jensenmath.

### Why do we study trigonometry?

Trigonometry is used to set directions such as the north south east west, it tells you what direction to take with the compass to get on a straight direction. It is used in navigation in order to pinpoint a location. It is also used to find the distance of the shore from a point in the sea.

### Is trigonometry hard without calculator?

However, trigonometry sums can be solved without the help of a calculator too. And though unbelievable, it’s not as hard as it seems to be. All you have to do is use the Trigonometry table and you will be able to crack up most of the answers in a short time and let me tell you that it’s even fun.

#### Why is infinity 1 0?

Hint: We need to find the value of 1 divided by 0. We start to perform a division considering number 1 as a dividend and the number 0 as a divisor. Then, we write all the cases encountered during the division to get the desired result. Complete step by step solution: The division of a real number $P$ with the real number $Q$ is given as follows, $\Rightarrow \dfrac $ Here, $P$ is the dividend of the division $Q$ is the divisor of the division Assuming the real number $R$ is the result of the above division.

Writing the expression for the same, we get, $\Rightarrow \dfrac =R$ Cross-multiplying the number $Q$ to the other side of the equation, $\Rightarrow P=Q\times R$ Now, According to our question, Assume that the value of $Q$ is equal to 0. $\Rightarrow Q=0$ If $P$ is the non-zero real number, there is no value of $R$ such that, if multiplied by the number $Q=0$, gives a non-zero real number $P$ since the product of any number with the number 0 is always 0.

Even if we consider the value of $P=0$, the real number $R$ can take any number that is multiplied by $Q=0$ to give the result as the number 0. From the above cases, We can say that the division by the number 0 is undefined among the set of real numbers.

- Therefore$ The result of 1 divided by 0 is undefined.
- Note: We must remember that the value of 1 divided by 0 is infinity only in the case of limits.
- The word infinity signifies the length of the number.
- In the case of limits, we only assume that the value of limit x tends to something and not equal to something.

So, we consider it infinity. In normal cases, the value of 1 divided by 0 is undefined.

### Why is tan 270 an error?

What is the Value of Tan 270 Degrees? – The value of tan 270 degrees is undefined. Tan 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238,,) We know, using degree to radian conversion, θ in radians = θ in degrees × ( pi /180°) ⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123,, ∴ tan 270° = tan(4.7123) = undefined Explanation: For tan 270 degrees, the angle 270° lies on the negative y-axis. Thus tan 270° value is not defined. Since the tangent function is a periodic function, we can represent tan 270° as, tan 270 degrees = tan(270° + n × 180°), n ∈ Z. ⇒ tan 270° = tan 450° = tan 630°, and so on. Note: Since, tangent is an odd function, the value of tan(-270°) = -tan(270°) = undefined.

## Why is tan 180 zero?

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°

## What is the easiest way to remember trigonometry?

The sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, for instance SOH-CAH-TOA in English: Sine = Opposite ÷ Hypotenuse. Cosine = Adjacent ÷ Hypotenuse. Tangent = Opposite ÷ Adjacent.

## What is the trick to remember trigonometric ratios Class 10?

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) | 0° | 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 0ol>

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.

- 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.

- 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.

- 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.

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.

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

- 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.

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- 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 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 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 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.

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- 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.

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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.

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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.