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Question

Use identities to write the equation  in terms of the single angle . Then solve the equation for 0 £  < 2p.

Answer 1

cos(2θ) = 2sin²θ

1 - 2sin²θ = 2sin²θ

4sin²θ = 1

sinθ = ±1/2

If sinθ = 1/2, then θ = π/6 or 5π/6

If sinθ = -1/2, then θ = 7π/6 or 11π/6

Answer 2

cos 2θ = 2 sin² θ

1 - 2 sin² θ = 2 sin² θ double angle formula

1 = 4 sin² θ

0.25 = sin² θ

±0.5 = sin θ

Can you determine θ and answer?