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Problem : Calculate sin(θ), cos(θ), and tan(θ) if sin(2θ) = 2 sin(30o)cos(30o).

2 sin(30o)cos(30o) = sin(2×30o). θ = 30o.sin(θ) = , cos(θ) = , and tan(θ) = .

Problem : Calculate cos(15o) using the fact that cos(30o) = .

cos(15o) = = .9659.

Problem : θ is in the first quadrant, and tan(θ) = . Find the sine, cosine, and tangent of 2θ.

sin(θ) = . cos(θ) = . With these values, we can calculate sine, cosine, and tangent of 2θ. sin(2θ) = 2 sin(θ)cos(θ) 0.4283. cos(2θ) = cos2(θ) - sin2(θ) - 0.9036. tan(2θ) = - 0.4740.

Problem : θ is in the third quadrant, and sin(θ) = - . Find the sine, cosine, and tangent of (θ).

cos(θ) = - . sin(θ) = = . cos(θ) = - = - . tan(θ) = - = - 3.
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