Trigonometry - Simple Identities (AQA 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 sec⁡θ\sec \theta in terms of cos⁡θ\cos \theta?

1cos⁡θ\frac{1}{\cos \theta}

Which quotient identity expresses tan⁡θ\tan \theta?

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

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

cos⁡θ\cos \theta

Which statement about cos⁡(−θ)\cos(-\theta) is correct?

cos⁡(−θ)=cos⁡θ\cos(-\theta) = \cos \theta

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

2sin⁡θcos⁡θ2 \sin \theta \cos \theta

What does the symbol ≡\equiv mean in trigonometry?

Identical to (true for all values)

If an equation has squared trig functions, which identity should you typically use first?

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

If sin⁡θ=12\sin \theta = \frac{1}{2} and θ\theta is obtuse, what is cos⁡θ\cos \theta?

−32-\frac{\sqrt{3}}{2}

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