**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**

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