CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

The question is from CAT Geometry - Trigonometry. This is about trigonometric functions. We need to find out the smallest possible value of the constant. Trigonometry is an important topic for CAT Preparation for the CAT Exam. Trigonometric ideas can be completely opposite, as in, some questions test lot of common sense with direction, heights and distances, while others could test you on identities. CAT exam could test one on both these fronts. Make sure you master both in CAT - Trigonometry.

Question 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

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : aSinx + bcosx can take a range of values. What is the possible range in this scenario?

3sinx + 4cosx ≥ -r
5(\\frac{3}{5}\\)sinx + \\frac{4}{5}\\)cosx) ≥ -r
\\frac{3}{5}\\) = cosA => sinA =\\frac{4}{5}\\)
5(sinx cosA + sinA cosx) ≥ -r
5(sin(x + A)) ≥ -r
5sin (x + A) ≥ -r
-1 ≤ sin (angle) ≤ 1
5sin (x + A) ≥ -5
r_min = 5

The question is "What is the smallest value ‘r’ can to take?"

Hence, the answer is 5.

Choice A is the correct answer.