Answer:
θ = {0, 3π/2} +2kπ
Step-by-step explanation:
For solving problems involving a linear combination of sine and cosine, it can be helpful to use the identity ...
[tex]a\sin{\theta}+b\cos{\theta}=c\sin{(\theta+\phi)} \quad\text{where $c=\sqrt{a^2+b^2}$ and $\phi=\tan^{-1}(b/a)$}[/tex]
Filling in the numbers, we have ...
[tex]a=-1,b=1,c=\sqrt{2},\phi=\tan^{-1}{(-1)}=\dfrac{3\pi}{4}\\\\\sqrt{2}\sin{(\theta+\frac{3\pi}{4})}=1\\\\\text{Solve for $\theta$:}\\\\\theta+\frac{3\pi}{4}=\sin^{-1}{(\frac{1}{\sqrt{2}})}\\\\\theta=\{\frac{\pi}{4},\frac{3\pi}{4}\}-\frac{3\pi}{4}+2k\pi\\\\\theta=\{0,\frac{3\pi}{2}\}+2k\pi\\\\\theta\approx \{0,4.712\}+6.283k[/tex]
