Trigonometry Crush 9

Geometry Level 4

If $5\cos x + 12\sin x = k$ , then number of integral values of $k$ is:

13 14 26 27

2 solutions

Raj Rajput
Jan 26, 2016

Done using same method(i.e by finding range), but in a hurry I forgot to include 0 and chose 26 as the answer. Xd!

Shivansh Jaiswal - 4 years, 10 months ago

@Calvin Lin Sir , how can I add details about my whole set of problems on this topic. Like "for more problems try this set "

RAJ RAJPUT - 5 years, 4 months ago

Rishabh Jain
Jan 26, 2016

Equation can be written as:

13 sin(x+ $\tan^{-1}(\frac{5}{12})~$ )=k

and we know range of sin x is [-1,1]

Hence $-13 \leq 13\sin x \leq 13$

Or $-13\leq k \leq 13$

No. Of integers= 2 $\times$ 13+1= $\large \boxed{27}$