CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Trigonometry

The question is from CAT Geometry - Trigonometry. This is about Maximum and Minimum Value of a Trigonometric Function. 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 4: Find the maximum and minimum value of 8 cos A + 15 sin A + 15

1. 11√2+15
2. 30; 8
3. 32; -2
4. 23; 8

Explanatory Answer

Method of solving this CAT Question from CAT Geometry - Trigonometry : Can we use pythagorean triplets here? Think!!

Always look out for Pythagorean triplets, we know that (8,15,17) is one
∴ The expression becomes: 17 (\\frac{8}{17}\\) Cos�A +\\frac{15}{17}\\) SinA)
Let there be a angle B for which sin B = \\frac{8}{17}\\), cos B = \\frac{15}{17}\\)
=> 17( sin B cos A + cos B sin A) + 15
17(sin(A+B)) + 15

We know that sin(A+B)_max = 1
sin(A+B)_min = -1

∴ Max value = 17 * 1 +15 = 32
Min value = 17 * -1 + 15 = -2

The question is "to find the maximum and minimum value "

Hence, the answer is 32; -2

Choice B is the correct answer.