Strategy for Trigonometric Equations (AQA A-Level Mathematics): Flashcards

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Strategy for Trigonometric Equations
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Example of linear trig equation

sinθ=12\sin\theta = \frac{1}{2}

Example of quadratic trig equation

2sin2θsinθ1=02\sin^2\theta - \sin\theta - 1 = 0

Pythagorean identity

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

Tangent identity (sin/cos form)

tanθ=sinθcosθ\tan\theta = \frac{\sin\theta}{\cos\theta}

Double angle identity for sine

sin(2θ)=2sinθcosθ\sin(2\theta) = 2\sin\theta\cos\theta

General solution: sinθ=k\sin\theta = k or cosθ=k\cos\theta = k

θ=θ0+360°n\theta = \theta_0 + 360°n (also check 180°θ0180° - \theta_0)

General solution: tanθ=k\tan\theta = k

θ=θ0+180°n\theta = \theta_0 + 180°n (or θ0+πn\theta_0 + \pi n)

Typical interval for trig solutions

0° to 360°360° or 00 to 2π2\pi radians

Compound angle (trig equations)

Angle more complicated than just θ\theta

First step solving compound angle equations

Modify domain to find limits for compound angle

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