Compound Angle Formulae (Leaving Cert Mathematics): Quizzes

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Compound Angle Formulae
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What is the formula for sin⁡(A+B)\sin(A + B)?

sin⁡Acos⁡B+cos⁡Asin⁡B\sin A \cos B + \cos A \sin B

What is the formula for cos⁡(A−B)\cos(A - B)?

cos⁡Acos⁡B+sin⁡Asin⁡B\cos A \cos B + \sin A \sin B

What is the formula for tan⁡(A+B)\tan(A + B)?

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

In cos⁡(A+B)=cos⁡Acos⁡B−sin⁡Asin⁡B\cos(A + B) = \cos A \cos B - \sin A \sin B, what sign appears in cos⁡(A−B)\cos(A - B)?

The minus becomes a plus

Using compound angle formulae, sin⁡(75°)=sin⁡(45°+30°)\sin(75°) = \sin(45° + 30°) equals what?

6+24\frac{\sqrt{6} + \sqrt{2}}{4}

What does cos⁡(45°−30°)\cos(45° - 30°) simplify to?

6+24\frac{\sqrt{6} + \sqrt{2}}{4}

What does sin⁡45°cos⁡15°−cos⁡45°sin⁡15°\sin 45° \cos 15° - \cos 45° \sin 15° equal?

sin⁡30°\sin 30°

How is the tangent compound angle formula derived?

By dividing sine formula by cosine formula

Do ordinary rules of algebra apply when expanding sin⁡(A±B)\sin(A \pm B)?

No, they do not apply

What does sin⁡(θ+π2)\sin(\theta + \frac{\pi}{2}) simplify to?

cos⁡θ\cos \theta

Which is NOT listed as an application of compound angle formulae?

Finding derivatives of functions

What Pythagorean identity is used in deriving compound angle formulae?

sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1

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