# Online Trigonometry Tutoring : Trigonometric Functions

Home | Online Math Tutoring | Online Trigonometry Tutoring | **Trigonometric Ratios (Or Functions)**

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## Learn about trigonometric ratios from certified online trigonometry tutor

**✓ **Trigonometric Ratios or Functions are special measurements of a **right triangle**

**✓ **The three basic trigonometric ratios are **sine, cosine and tangent**

**✓ In a right angled triangle we can define all the trigonometric ratios.**

### Definitions of Trigonometric Ratios

**Sine****is**defined as the ratio of the side opposite to that angle to the hypotenuse.**Cosine****is**defined as the ratio of the side adjacent to that angle to the hypotenuse.**Tangent****is**defined as the ratio of the side opposite to that angle to the side adjacent to that angle.**Cosecant**is the multiplicative inverse of sine.**Secant**is the multiplicative inverse of cosine.**Cotangent**is the multiplicative inverse of tangent.

### Examples

A. List the values of sin A, cos A, tan A for the triangle when length is given as 9.2

**Hypo****tenuse= 9.2**

For sin A = Opposite/Hypotenuse = 6.0/9.2 = 0.652

For cos A= Adjacent/Hypotenuse = 7.2/9.2 = 0.782

For tan A = Adjacent/Opposite = 7.2/6.0 = 1.2

**Problem 1. In this triangle, find the value of x.**

Given : Length of the side= 45

angle = 30°

To Calculate: hypotenuse which is *x*?

Sin (30) = Opposite/Hypotenuse

= 45/*x*

*x* = 45/sin (30)

= 90

**Check Point**

Problem 1. If *x* is an acute angle and tan *x* = 6, find the exact value of the trigonometric functions sin *x* and cos *x*.

Problem 2. What is the value of cos A ,cot A and sec A in given triangle?

Problem 3. State True or False

i) Ratio of the side adjacent to that angle to the hypotenuse is sine. _________

ii) Cotangent is a multiplicative inverse of tangent. ________

##### Answer Key

Answer 1. sin *x* = 0.98, cos *x* = 0.16

Answer 2. cos (A) = 0.5

sec (A) = 2

cot (A) = 1/

Answer 3. i) False

ii) True

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