Trigonometric Equations (AQA A-Level Mathematics): Quizzes

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Trigonometry - Simple Identities
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What is the basic Pythagorean identity?

sin2θ+cos2θ=1\sin^2 \theta + \cos^2 \theta = 1

Which identity is obtained by dividing sin2θ+cos2θ=1\sin^2 \theta + \cos^2 \theta = 1 by cos2θ\cos^2 \theta?

1+tan2θ=sec2θ1 + \tan^2 \theta = \sec^2 \theta

What is secθ\sec \theta in terms of cosθ\cos \theta?

1cosθ\frac{1}{\cos \theta}

Which quotient identity expresses tanθ\tan \theta?

sinθcosθ\frac{\sin \theta}{\cos \theta}

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

cosθ\cos \theta

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

cos(θ)=cosθ\cos(-\theta) = \cos \theta

What is the double angle identity for sin2θ\sin 2\theta?

2sinθcosθ2 \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?

sin2θ+cos2θ=1\sin^2 \theta + \cos^2 \theta = 1

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

32-\frac{\sqrt{3}}{2}

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