# CAT Practice : Trigonometry

You are here: Home  CAT Questionbank   CAT Quant  Geometry: Trigonometry  Question 1
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

Choice A. 5

## Detailed Solution

3sinx + 4cosx ≥ -r
5$\left( {{{\rm{3}} \over {\rm{5}}}{\rm{ sinx + }}{{\rm{4}} \over {\rm{5}}}{\rm{ cosx}}} \right)$ ≥ -r
${{{\rm{3}} \over {\rm{5}}}}$ = cosA => sinA =${{{\rm{4}} \over {\rm{5}}}}$
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

## Our Online Course, Now on Google Playstore!

### Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

### Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

## More questions from Trigonometry

Trigonometry..........