TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES WORKSHEET

Problem 1 :

Evaluate :

cos56°/sin34°

Problem 2 :

Evaluate :

tan25°/cot65°

Problem 3 :

Evaluate :

(cos65°sin18°cos58°)/(cos72°sin25°sin32°)

Problem 4 :

Evaluate :

tan35°tan60°tan55°tan30°

Problem 5 :

If sinA = cos33°, find A.

Problem 6 :

If tanAtan35° = 1, find A.

Answers

1. Answer :

cos56°/sin34°

The angles 56° and 34° are complementary.

Use trigonometric ratios of complementary angles. 

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

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

cos 56° / sin 34°  =  1

2. Answer :

tan25°/cot65°

The angles 25° and 65° are complementary.

Use trigonometric ratios of complementary angles.

tan25°/cot65° = tan25°/tan(90° - 65°)

= tan 25°/tan 25°

= 1

3. Answer :

(cos65°sin18°cos58°)/(cos72°sin25°sin32°)

Using trigonometric ratios of complementary angles, we have

cos65° = cos(90° - 25°) = sin25°

sin18° = sin(90° - 72°) = cos72°

cos58° = cos(90° - 32°) = sin32°

(cos65°sin18°cos58°)/(cos72°sin25°sin32°) is

= (sin25°cos72°sin32°)/(cos72°sin25°sin32°)

= 1

So,

(cos65°sin18°cos58°)/(cos72°sin25°sin32°) = 1

4. Answer :

tan35°tan60°tan55°tan30°

tan35° = tan(90° - 55°) = cot55° = 1/tan55°

tan60° = tan(90° - 30°) = cot30° = 1/tan30°

tan35°tan60°tan55°tan30° :

= (1/tan55°) x (1/tan30°)tan55°tan30°

= 1

So,

tan35°tan60°tan55°tan30° = 1

5. Answer :

sinA = cos33°

sinA = sin(90° - 33°) 

  sinA = sin57°

A = 57°

6. Answer :

tanAtan35° = 1

Divide  each side by tan 35°.

tanA = 1/tan35°

tanA = cot35°

tanA = tan(90° - 35°)

tanA = tan55°

A = 55°

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