Trigonometric ratios of complementary angles MCQs

Q1. A bridge engineer needs to swap sin 23 deg for the matching ratio of its complement; which value is identical?

• A.cos 67 deg
• B.sin 67 deg
• C.cos 157 deg
• D.cos 23 deg

Answer: A. cos 67 deg

Complementary-angle rule: sin(t) = cos(90 - t). Put t = 23, so sin 23 deg = cos 67 deg.

Q2. Rewriting cos 31 deg through the angle that completes it to a right angle, what equal ratio appears?

• A.sin 149 deg
• B.sin 59 deg
• C.cos 59 deg
• D.sin 31 deg

Answer: B. sin 59 deg

Complementary-angle rule: cos(t) = sin(90 - t). Put t = 31, so cos 31 deg = sin 59 deg.

Q3. To merge two terms a coder substitutes tan 18 deg with the co-ratio of (90 - 18) deg; what does it become?

• A.tan 72 deg
• B.cot 162 deg
• C.cot 18 deg
• D.cot 72 deg

Answer: D. cot 72 deg

Complementary-angle rule: tan(t) = cot(90 - t). Put t = 18, so tan 18 deg = cot 72 deg.