Trigonometric ratios MCQs

Q1. The value of sin A can never exceed:

• A.0
• B.the hypotenuse
• C.90
• D.1

Answer: D. 1

NCERT fact (math, chapter 'Introduction to Trigonometry'): Recall that in a right triangle with legs p, b and hypotenuse h: sin = p/h, cos = b/h, tan = p/b; identify the side-pair demanded and read off the ratio => the required value follows directly; so the answer = 1. Why option D fits - Correct. Distractor analysis: option A) '0' fails since sin ranges in [-1,1]; max 1; option B) 'the hypotenuse' is wrong because sin is a ratio <= 1. Final answer - D) 1.

Q2. cosec A is the reciprocal of:

• A.sin A
• B.tan A
• C.sec A
• D.cos A

Answer: A. sin A

Which principle settles this? Recall that in a right triangle with legs p, b and hypotenuse h: sin = p/h, cos = b/h, tan = p/b; identify the side-pair demanded and read off the ratio => the required value follows directly; so the answer = sin A. Does that line up with one of the options? Yes - Correct. And the rest? option B) 'tan A' misses the point - cot is reciprocal of tan; option C) 'sec A' is wrong because cosec = 1/sin. Pick: A) sin A.

Q3. sec A is the reciprocal of:

• A.cot A
• B.tan A
• C.sin A
• D.cos A

Answer: D. cos A

Eliminate first - option A) 'cot A' doesn't hold - sec = 1/cos; option B) 'tan A' is incorrect: cot = 1/tan; option C) 'sin A' doesn't hold - cosec = 1/sin. That leaves only option D). Confirm with the chapter rule: Recall that in a right triangle with legs p, b and hypotenuse h: sin = p/h, cos = b/h, tan = p/b; identify the side-pair demanded and read off the ratio => the required value follows directly; so the answer = cos A (math, chapter 'Introduction to Trigonometry'). Answer: D) cos A.