More Trigonometric Identities

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

Solution for Problem 1 >>

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

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

Solution for Problem 2 >>

cos(15 ^o ) = = .9659 .

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

Solution for Problem 3 >>

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 .

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

Solution for Problem 4 >>

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

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