Question

Use identities to write each equation in terms of the single angle θ. Then solve the equation for 0≤θ<2π . 2 sin 2θ-3sinθa=0

Answer 1

Explanation:

2 sin 2θ-3sinθa=0

2(2sinθcosθ)-3sinθa=0

4sinθcosθ-3sinθa=0

We are taking 2 as identity.

After this, we need to factorize

4sinθcosθ-3sinθa=0

sinθ(4cosθ-3a)=0

Either sinθ=0 or 4cosθ-3a=0:

If sinθ=0, then θ=0 or θ=180°.

If 4cosθ-3a=0, then cosθ=3a/4.

The solutions in the interval 0≤θ<2π are θ=30° and θ=150°.

Therefore, the solutions to the equation are θ=0°, θ=180°, θ=30°, and θ=150°.