Answer to Question #311453 in Trigonometry for bookaddict

Question

Solve the equation √3sin𝜃−cos𝜃=0 for −180°≤𝑥≤180°

Answer 1

$\sqrt{3} \sin\theta=\cos \theta;\\ \cfrac{\sin\theta}{\cos\theta}=\cfrac{1}{\sqrt3};\\ \tan\theta=\cfrac{1}{\sqrt3};\\ \theta=\arctan\cfrac{1}{\sqrt3}+180\degree\cdot n=30\degree+180\degree\cdot n, \ \ n\in Z;\\$

for $-180\degree\leq\theta\leq180\degree\ \ n=0$ or $n=-1;$

$\theta_1=-150\degree,\ \ \theta_2=30\degree.$