Contents

Ratio for Acute Angles

Ratio for General Angles

1  2

Ratio for Negative Angles

Ratio for Special Angles

Ratio for Complementary Angles

Other Trigonometry Ratios

Inverse Functions

Quiz 

Trigonometry Main Page

Trigonometric Ratio of General Angles 2

The relationship given the page before connecting any angle and a basic angle are summarized in the diagram below. These results are very important and should be remembered.

Example 1

Express sin 323°, tan 98° and cos 236° in terms of the ratios of their basic angles.

sin 323° = - sin(360° - 323°) = - sin 37°

    cos 236° = cos(236° - 180°) = - cos 56°

    tan 98° = tan(180° - 98°) = - tan 82° 

 

Example 2

 

Given that cos = -4/5 and 180°< q  <270°, evaluate tan q and sin q.

  q is in the third quadrant 

     cos q = - cos a = -4/5

                  cos a = 4/5

 

     Let OQ = 4 units and OP = 5 units.

     By Pythagoras's theorem,

     PQ = 3

     tan q = tan a = ¾

Example 3

Given that A is obtuse and than tan A = -½, find the values of cos A and of sin A. 

Let OQ = 2 units, PQ = 1 unit

PQ =

cos A =

sin A =