# Math Help - trig putting in for rcos(x-a)

1. ## trig putting in for rcos(x-a)

Hello

I need help with some this type of trig question

can you someone please go throught the process of solving it so thats its in the form that is required. I am unsure on how to do these type of questions

thanks

2. Hi

$a cos x + b sin x = \sqrt{a^2 + b^2} \:\left( \frac{a}{\sqrt{a^2 + b^2}} cos x + \frac{b}{\sqrt{a^2 + b^2}} sin x \right)$

$\frac{a}{\sqrt{a^2 + b^2}}$ and $\frac{b}{\sqrt{a^2 + b^2}}$ can be seen respectively as the cosines and the sinus of the same angle $\theta$ because the sum of their square is equal to 1

Therefore

$a cos x + b sin x = \sqrt{a^2 + b^2} \:\left( cos \theta cos x + sin \theta sin x \right) = \sqrt{a^2 + b^2} \:cos(x-\theta)$