Sum and difference of two angles (HSC SSCE Mathematics Extension 1): Quizzes

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Sum and Difference of Two Angles
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What is the sine sum identity formula?

sin(θ + φ) = sin θ cos φ + cos θ sin φ

What is the cosine difference identity for cos(θ - φ)?

cos θ cos φ + sin θ sin φ

How is tan(θ + φ) derived?

tan(θ + φ) = sin(θ + φ)/cos(θ + φ)

What is the formula for sin(θ - φ)?

sin(θ - φ) = sin θ cos φ - cos θ sin φ

What is the correct cosine sum identity formula?

cos(θ + φ) = cos θ cos φ - sin θ sin φ

What is the tangent difference identity?

tan(θ - φ) = (tan θ - tan φ)/(1 + tan θ tan φ)

What is sin(75°) using identities?

sin(45° + 30°)

What does sin(40°) cos(10°) + cos(40°) sin(10°) equal?

sin(50°)

What is the purpose of trigonometric identities?

To simplify trigonometric functions

What aids in visualizing angles in trigonometry?

Unit circle diagrams

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