Trigonometric ratios of complementary anglesPractice Questions & MCQs

Q1. Evaluate (use sin(90-x)=cos x etc.): sin 12 / cos 78

• A.0
• B.3
• C.1
• D.2

Answer: C. 1

Q2. The value of tan 12 . cot 12 is:

• A.3
• B.0
• C.2
• D.1

Answer: D. 1

Given 12, 12, asked for the unknown. By recall that in a right triangle with legs p, b and hypotenuse h: sin = p/h, cos = b/h, tan = p/b. so the answer = 1. identify the side-pair demanded and read off the ratio. Therefore option D) 1. Others fail: option A) '3' fails since Wrong: a common multi-step slip gives this; option B) '0' is wrong because Wrong: uses an incorrect intermediate value.

Q3. Evaluate (use sin(90-x)=cos x etc.): sin 12 . sec 78

• A.0
• B.3
• C.1
• D.2

Answer: C. 1

Given 90, 12, 78, asked for Evaluate (use sin(90-x)=cos x etc. By use complementary-angle identities sin(90-x)=cos x, cos(90-x)=sin x, tan(90-x)=cot x. use complementary-angle identities sin(90-x)=cos x, cos(90-x)=sin x, tan(90-x)=cot x → the expression collapses via sin^2 + cos^2 = 1 or tan*cot = 1 → hence the value = 1. rewrite each term in the expression with this substitution. Consequently option C) 1. Others fail: option A) '0' misses the point - Wrong: uses an incorrect intermediate value; option B) '3' is wrong because Wrong: a common multi-step slip gives this.