# Online Trigonometry Tutoring : Trigonometric Functions

**Trigonometric Ratios (Or Functions)**

**Simplify trigonometry. **Our expert and qualified** **trigonometry tutors understand your problems and guide you towards better grades in trigonometry. Our aim is to help the student understand concepts in trigonometry and master the techniques of solving problems quickly with confidence.

## 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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