Strategy for 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 sin⁡2θ\sin 2\theta?

2sin⁡θcos⁡θ2\sin \theta \cos \theta

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

2cos⁡2θ−12\cos^2 \theta - 1

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

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

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

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

What technique is useful for quadratic forms like sin⁡2θ\sin^2 \theta and sin⁡θ\sin \theta?

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

When do extraneous solutions often arise?

When squaring both sides of an equation

In R addition formula, what is RR for acos⁡θ+bsin⁡θ=ca \cos \theta + b \sin \theta = c?

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

In R addition formula, what is tan⁡α\tan \alpha for acos⁡θ+bsin⁡θa \cos \theta + b \sin \theta?

ba\frac{b}{a}

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

sin⁡Acos⁡B+cos⁡Asin⁡B\sin A \cos B + \cos A \sin B

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