Trig Help!

[mike430]

Solve equation for exact solutions if possible put answer in degrees

sin x/2= square root of 2 -sin x/2

I do not understand this problem at all.

 

[soroban]

Hello, mike430!

Solve equation for exact solutions if possible put answer in degrees

. . \(\displaystyle \sin\frac{x}{2}\:=\: \sqrt{2} -\sin\frac{x}{2}\)

I do not understand this problem at all.

What part don't you understand?

We have an equation of the form: .\(\displaystyle Y \:=\:\sqrt{2} - Y\)
Can you solve for \(\displaystyle Y\) ?

If you do, we get: .\(\displaystyle 2\sin\frac{x}{2} \:=\:\sqrt{2} \quad\Rightarrow\quad \sin\frac{x}{2} \:=\:\frac{\sqrt{2}}{2}\,\text{ or }\,\frac{1}{\sqrt{2}}\)

Now, what angles have a sine of \(\displaystyle \frac{1}{\sqrt{2}}\,?\)
. . . and so on . . .