Products to Sums and Differences (Leaving Cert Mathematics): Quizzes

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Products to Sums and Differences
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What do products to sums formulas transform?

Products of trig functions to sums

What is sin⁡Acos⁡B\sin A \cos B equal to?

12[sin⁡(A+B)+sin⁡(A−B)]\frac{1}{2}[\sin(A+B) + \sin(A-B)]

What is cos⁡Asin⁡B\cos A \sin B equal to?

12[sin⁡(A+B)−sin⁡(A−B)]\frac{1}{2}[\sin(A+B) - \sin(A-B)]

What is cos⁡Acos⁡B\cos A \cos B equal to?

12[cos⁡(A+B)+cos⁡(A−B)]\frac{1}{2}[\cos(A+B) + \cos(A-B)]

What is sin⁡Asin⁡B\sin A \sin B equal to?

−12[cos⁡(A+B)−cos⁡(A−B)]-\frac{1}{2}[\cos(A+B) - \cos(A-B)]

What identities are used to derive products to sums formulas?

Addition and subtraction identities

Which field uses products to sums formulas?

Signal processing

Simplify sin⁡3xcos⁡2x\sin 3x \cos 2x using products to sums.

12[sin⁡5x+sin⁡x]\frac{1}{2}[\sin 5x + \sin x]

Simplify cos⁡4xcos⁡2x\cos 4x \cos 2x using products to sums.

12[cos⁡6x+cos⁡2x]\frac{1}{2}[\cos 6x + \cos 2x]

What is a key benefit of using products to sums formulas?

Simplify trigonometric expressions

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