Compound Angle Formulae (Edexcel A-Level Mathematics): Flashcards

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Compound Angle Formulae
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What is the sine sum formula for angles AA and BB?

sin⁡(A+B)=sin⁡Acos⁡B+cos⁡Asin⁡B\sin(A + B) = \sin A \cos B + \cos A \sin B

What is the sine difference formula for angles AA and BB?

sin⁡(A−B)=sin⁡Acos⁡B−cos⁡Asin⁡B\sin(A - B) = \sin A \cos B - \cos A \sin B

State the cosine sum formula for angles AA and BB.

cos⁡(A+B)=cos⁡Acos⁡B−sin⁡Asin⁡B\cos(A + B) = \cos A \cos B - \sin A \sin B

What is the cosine difference formula for angles AA and BB?

cos⁡(A−B)=cos⁡Acos⁡B+sin⁡Asin⁡B\cos(A - B) = \cos A \cos B + \sin A \sin B

State the tangent sum formula for angles AA and BB.

tan⁡(A+B)=tan⁡A+tan⁡B1−tan⁡Atan⁡B\tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}

What is the tangent difference formula for angles AA and BB?

tan⁡(A−B)=tan⁡A−tan⁡B1+tan⁡Atan⁡B\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}

How can compound angle formulae be derived?

By using the unit circle and trigonometric identities.

What is sin⁡(A+B)\sin(A + B) in terms of AA and BB?

sin⁡(A+B)=sin⁡Acos⁡B+cos⁡Asin⁡B\sin(A + B) = \sin A \cos B + \cos A \sin B

What is cos⁡(A+B)\cos(A + B) in terms of AA and BB?

cos⁡(A+B)=cos⁡Acos⁡B−sin⁡Asin⁡B\cos(A + B) = \cos A \cos B - \sin A \sin B

What applications do compound angle formulas have?

Solved trigonometric equations and proved identities.

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