Question

Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to three decimal places where appropriate.)
sin 2θ + sin θ = 0

Answer 1

sin2x = 2sinx cosx
so, you have
2sinx cosx + sinx = 0
sinx (2cosx+1) = 0

you should be able to sort that out easily, looking for values where
sinx=0 or cosx = -1/2

Answer 2

If a projectile is fired with velocity v0 at an angle θ, then its range, the horizontal distance it travels (in feet), is modeled by the function
R(θ) =
v02 sin 2θ
32
.
If
v0 = 2600 ft/s,
what angle (in degrees) should be chosen for the projectile to hit a target on the ground 5000 ft away? (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
Thanks.