Online Trigonometry Tutoring : Trigonometric 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.

Right Angle Triangle

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.


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

Hypotenuse= 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/\sqrt{3}

Answer 3. i) False

ii) True

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