Strategy for Further Trigonometric Equations (Edexcel A-Level Mathematics): Quizzes

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Strategy for Further Trigonometric Equations
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What is the double-angle identity for sin⁡2θ\sin 2\theta?

2sin⁡θcos⁡θ2\sin \theta \cos \theta

Which expression is NOT a double-angle identity for cos⁡2θ\cos 2\theta?

2sin⁡θcos⁡θ2\sin \theta \cos \theta

What does sin⁡Asin⁡B\sin A \sin B equal using product-to-sum identities?

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

When solving equations quadratic in form, what substitution technique is used?

Let u=sin⁡θu = \sin \theta or cos⁡θ\cos \theta

Why must we consider general solutions when solving trigonometric equations?

Trigonometric functions are periodic

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

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

For sin⁡θ=k\sin \theta = k, what is one form of the general solution?

θ=θ0+360∘n\theta = \theta_0 + 360^\circ n

Why should solutions be substituted back into the original equation?

To check for extraneous solutions

In the R addition formula, what does RR equal for acos⁡θ+bsin⁡θa \cos \theta + b \sin \theta?

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

In the R addition formula, what does tan⁡α\tan \alpha equal?

ba\frac{b}{a}

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