Trigonometric Equations (Edexcel A-Level Mathematics): Quizzes

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Strategy for Trigonometric Equations
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What type of equation is 2sin2θsinθ1=02\sin^2 \theta - \sin \theta - 1 = 0?

Quadratic

Which identity relates sin2θ\sin^2 \theta and cos2θ\cos^2 \theta?

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

For tanθ=k\tan \theta = k, what is the general solution?

θ=θ0+180n\theta = \theta_0 + 180^\circ n

What is the double-angle identity for sin(2θ)\sin(2\theta)?

2sinθcosθ2\sin \theta \cos \theta

What is the typical interval for listing trig equation solutions in degrees?

00^\circ to 360360^\circ

For 2sin2θ3sinθ+1=02\sin^2 \theta - 3\sin \theta + 1 = 0, which are the solutions in 0θ3600^\circ \leq \theta \leq 360^\circ?

30,90,15030^\circ, 90^\circ, 150^\circ

What is a compound angle in trigonometry?

An angle more complicated than just θ\theta

For sin(3θ)=0.42\sin(3\theta) = 0.42 with 0θ1800 \leq \theta \leq 180, what is the domain for 3θ3\theta?

03θ5400 \leq 3\theta \leq 540

For sinθ=k\sin \theta = k, which angles are primary solutions?

θ0\theta_0 and 180θ0180^\circ - \theta_0

Why should solutions be verified in trig equations?

To ensure they satisfy the original eqn

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