Question

1 Find all solutions of the following equations in the interval [0, 2π)

(a) sin(2x) = √2 cos(x).

(b) 2 cos²(x) + 3 sin(x) = 3.

2. Sketch the graph of the circular function

F(Θ) = 1- 2cos (3Θ +π)

i. State clearly the amplitude, phase shift, period and the equation of the midline.

ii. Show working for all Θ- and y-intercepts for the function y = f(Θ).

iii. Show at least two periods for the graph of y = f(Θ), and label the axes clearly.

(b) Prove the following identity

2sin(1/2 (x+y))cos (1/2(x-y))= sin(X) +sin(y)

Make sure you show all working and give clear explanations.