CAT - Trigonometry Questions

Question:

3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?

A.  5

B.  -5

C.  4

D.  3

Correct Answer: (A)

Explanation:

3sinx + 4cosx ≥ -r

≥ -r

= cosA  => sinA =

5(sinx cosA + sinA cosA) ≥ -r

5(sin(x + A) ≥ -r

5sin (x + A) ≥ -r

-1 < sin (angle) < 1

5sin (x + A) ≥ -5

r_min = 5

Difficulty Level 2