Trigonometry - Simple Identities (Edexcel A-Level Mathematics): Quizzes

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Trigonometry - Simple Identities
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What is the basic Pythagorean identity?

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

Which identity is obtained by dividing sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1 by cos⁡2θ\cos^2 \theta?

1+tan⁡2θ=sec⁡2θ1 + \tan^2 \theta = \sec^2 \theta

What is the reciprocal identity for sin⁡θ\sin \theta?

csc⁡θ=1sin⁡θ\csc \theta = \frac{1}{\sin \theta}

What is the quotient identity for tan⁡θ\tan \theta?

tan⁡θ=sin⁡θcos⁡θ\tan \theta = \frac{\sin \theta}{\cos \theta}

What does sin⁡(90∘−θ)\sin(90^\circ - \theta) equal?

cos⁡θ\cos \theta

What is sin⁡(−θ)\sin(-\theta) equal to?

−sin⁡θ-\sin \theta

What is the double angle identity for sin⁡2θ\sin 2\theta?

sin⁡2θ=2sin⁡θcos⁡θ\sin 2\theta = 2 \sin \theta \cos \theta

What does the ≡\equiv sign mean in trigonometric identities?

Identical to; true for all values

Why is sin⁡θ+cos⁡θ≡1\sin \theta + \cos \theta \equiv 1 incorrect?

It's not an identity; only true for specific θ\theta

When solving sin⁡θ=3sin⁡θcos⁡θ\sin \theta = 3 \sin \theta \cos \theta, why must you factorise, not divide by sin⁡θ\sin \theta?

Dividing loses the solution where sin⁡θ=0\sin \theta = 0

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