CAT Practice : Trigonometry

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aSinx + bcosx can take range of values. What is this range?

Trigonometry - Sine and Cosine

    Q.1: 3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?
    1. 5
    2. -5
    3. 4
    4. 3

 

  • Correct Answer
    Choice A. 5

Detailed Solution

3sinx + 4cosx ≥ -r
5 ≥ -r
= cosA => sinA =
5(sinx cosA + sinA cosx) ≥ -r
5(sin(x + A)) ≥ -r
5sin (x + A) ≥ -r
-1 ≤ sin (angle) ≤ 1
5sin (x + A) ≥ -5
rmin = 5
Answer Choice (A)

Correct Answer: 5



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Trigonometry..........