Question

Trig help please?

Solve the system using algebra and trigonometry.

r = 2sin(theta)
r = 2sin2(theta)

Answer 1

sin(a+b) = sin(a)cos(b) + sin(b)cos(a)
sin(2a) = sin(a+a)

Answer 2

Solve the system: 2sin x = 2sin 2x -> sin x = 2*sin x*cos x =
sin x*(1 - 2cos x) = 0
a) sin x = 0 = sin 0; sin Pi or sin 2Pi -> x = 0, Pi, or 2Pi
b) (1 - 2cos x) = 0 -> cos x = 1/2 = cos Pi/3; and cos x = cos 5Pi/3
-> x = Pi/3 and x = 5Pi/3

Answer 3

Check the system with x = Pi/3.
y1 = 2sin x = 2*(V3/2) = V3
y2 = 2sin 2x = 2*sin (2PI/3) = 2(V3)/2) = V3.
So, Pi/3 is a true solution.