1. Help me please with triogonometry:)thank you

12 cos x - 5 sin x = R cos (x + 22.6)

solve x in range 0 to 360 degrees
(12 cos x- 5 sin x)^2

Also, find the max and min value of eqn.

Kindly explain it clearly because I actually got an explanation from somewhere but it is not clear. Thank you greatly for your help.God bless you.

2. The kind of structure you have on the left is very cooperative. It is simply transformed to the even more convenient form on the left.

$\displaystyle R = \sqrt{12^{2}+(-5)^{2}} = 13$

R = sqrt(12^2 + (-5)^2) = 13

The angle is a little trickier, but simply written.

theta = -atan(-5/12)

Then just write the answer 13*cos(x-theta)