Question

I just need a little help please. I have got the answer almost.

Answer 1

\[\cos (x+45)- \sqrt{2}\sin x=2\]

Answer 2

I solved the equation and got the answer of x= -45.0 degrees.
The question says give answer in the range 0<x<360. -45.0 means 315 degrees. But there is a second value of x=261.9. How do I get that?

Answer 3

I haven't figured out how to get to the other answer, but I can tell you that it is
\[x = -\cos^{-1}(-\frac{1}{5\sqrt{2}})\]

Answer 4

I figured it out. The values of cos^-1 in 1st quadrant gives x=-45.0, and in the third quadrant, would give me 261.9.
Thankyou.