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 sin2θ\sin 2\theta?

2sinθcosθ2\sin \theta \cos \theta

Which expression is NOT a double-angle identity for cos2θ\cos 2\theta?

2sinθcosθ2\sin \theta \cos \theta

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

12[cos(AB)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=sinθu = \sin \theta or cosθ\cos \theta

Why must we consider general solutions when solving trigonometric equations?

Trigonometric functions are periodic

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

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

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

θ=θ0+360n\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 acosθ+bsinθa \cos \theta + b \sin \theta?

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

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

ba\frac{b}{a}

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