Question

1) Find exact solution
a) Using identity:
sin x + Sqrt(3) cos x = 1, where 0 =< x =< 2pi

b) Using tan 2 thetha , thetha [-pi,pi] :
(2sin thetha)/cos thetha = tan^2 thetha - 1

c) Cos 4x = -2cos^2 x

Answer 1

rewrite \(\sin(x)+\sqrt{3}\cos(x)\) as \(r\sin(x+\theta)\)

Answer 2

\(r=\sqrt{1^2+\sqrt{3}^2}=\sqrt{4}=2\)

Answer 3

\(\sin(\theta)=\frac{\sqrt{3}}{2}\) and \(\cos(\theta)=\frac{1}{2}\) so \(\theta=\frac{\pi}{3}\)