Question

for what values of theta ,sin theta=2​

Answer 1

Step-by-step explanation:

sin 2θ = sin θ

But we know a formula for sin 2θ = 2 sin θ cosθ

Therefore we must solve 2 sin θ cosθ = sin θ.

Rearrange & factor: (sin θ) (2 cos θ - 1) = 0.

Using the Zero Product Property, your solutions are those which satisfy either of the following:

(sin θ) = 0 OR (2 cos θ - 1)= 0.

and

sin 2θ = sin θ

2 sin θ cos θ = sin θ double angle formula

2 sin θ cos θ - sin θ = 0 subtract sin θ from both sides

sin θ (2 cos θ - 1) = 0 GCF

sin θ = 0 zero product rule

2 cos θ - 1 = 0 zero product rule

2 cos θ = 1

cos θ = 0.5

θ = π/3

θ = 5π/3