# TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES WORKSHEET

Trigonometric Ratios of Complementary Angles Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on trigonometric ratios of complementary angles.

Before look at the worksheet, if you would like to learn trigonometric ratios of complementary angles,

## Trigonometric Ratios of Complementary Angles Worksheet - Problems

Problem 1 :

Evaluate :

cos 56° / sin 34°

Problem 2 :

Evaluate :

tan 25° / cot 65°

Problem 3 :

Evaluate :

(cos 65° sin 18° cos 58°) / (cos 72° sin 25° sin 32°)

Problem 4 :

Prove :

tan 35° tan 60° tan 55° tan 30°   =  1

Problem 5 :

If sin A  =  cos 33°, find A

## Trigonometric Ratios of Complementary Angles Worksheet - Solutions

Problem 1 :

Evaluate :

cos 56° / sin 34°

Solution :

The angles 56° and 34° are complementary.

Using trigonometric ratios of complementary angles,

cos 56°  =  cos (90° - 56°)  =  sin 34°

cos 56° / sin 34°  =  sin 34° / sin 34°  =  1

So, the value of cos 56° / sin 34° is 1.

Problem 2 :

Evaluate :

tan 25° / cot 65°

Solution :

The angles 25° and 65° are complementary.

Using trigonometric ratios of complementary angles,

tan 25°  =  tan (90° - 65°)  =  cot 65°

tan 25° / cot 65°  =  cot 65° / cot 65°  =  1

So, the value of tan 25° / cot 65° is 1.

Problem 3 :

Evaluate :

(cos 65° sin 18° cos 58°) / (cos 72° sin 25° sin 32°)

Solution :

Using trigonometric ratios of complementary angles,

cos 65°  =  cos (90° - 25°)  =  sin 25°

sin 18°  =  sin (90° - 72°)  =  cos 72°

cos 58°  =  cos (90° - 32°)  =  sin 32°

(cos 65° sin 18° cos 58°) / (cos 72° sin 25° sin 32°) is

=  (sin 25° cos 72° sin 32°) / (cos 72° sin 25° sin 32°)

=  1

So, the value of the given trigonometric expression is 1.

Problem 4 :

Prove :

tan 35° tan 60° tan 55° tan 30°   =  1

Solution :

Using trigonometric ratios of complementary angles,

tan 35°  =  tan (90° - 55°)  =  cot 55°  =  1/tan 55°

tan 60°  =  tan (90° - 30°)  =  cot 30°  =  1/tan 30°

tan 35° tan 60° tan 55° tan 30°  is

=  (1/tan 55° ) x (1/tan 30°) tan 55° tan 30°

=  1

So,

tan 35° tan 60° tan 55° tan 30°   =  1

Problem 5 :

If sin A  =  cos 33°, find A

Solution :

Using trigonometric ratios of complementary angles,

sin A  =  cos (90° - A)

Then,

sin A  =  cos 33°

cos (90° - A)  =  cos 33°

90° - A  =  33°

90° - 33°  =  A

57°  =  A

So, A is 57°.

After having gone through the stuff given above, we hope that the students would have understood, how to solve problems using trigonometric rations of compound angles.

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