Further Trigonometric Equations (AQA A-Level Mathematics): Quizzes

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Strategy for Further Trigonometric Equations
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What types of elements might further trig equations involve?

Multiple angles and double-angle identities

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

2sinθcosθ2\sin \theta \cos \theta

Which is a double-angle identity for cos2θ\cos 2\theta?

2cos2θ12\cos^2 \theta - 1

What is the product-to-sum identity for sinAsinB\sin A \sin B?

12[cos(AB)cos(A+B)]\frac{1}{2}[\cos(A-B) - \cos(A+B)]

What is the general solution for tanθ=k\tan \theta = k?

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

What technique is useful for quadratic forms like sin2θ\sin^2 \theta and sinθ\sin \theta?

Substitution (e.g., u=sinθu = \sin \theta)

When do extraneous solutions often arise?

When squaring both sides of an equation

In R addition formula, what is RR for acosθ+bsinθ=ca \cos \theta + b \sin \theta = c?

a2+b2\sqrt{a^2 + b^2}

In R addition formula, what is tanα\tan \alpha for acosθ+bsinθa \cos \theta + b \sin \theta?

ba\frac{b}{a}

What is the sum identity for sin(A+B)\sin(A + B)?

sinAcosB+cosAsinB\sin A \cos B + \cos A \sin B

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