Linear Trigonometric Equations (Edexcel A-Level Mathematics): Quizzes

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Linear Trigonometric Equations
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What defines a linear trigonometric equation?

Variable appears in linear form only

What is the period of tan⁡θ\tan \theta?

180∘180^\circ or π\pi radians

In which quadrants is sin⁡θ\sin \theta positive?

First and second quadrants

In which quadrants is cos⁡θ\cos \theta negative?

Second and third quadrants

What are the solutions to sin⁡θ=0.5\sin \theta = 0.5 for 0∘≤θ≤360∘0^\circ \leq \theta \leq 360^\circ?

30∘,150∘30^\circ, 150^\circ

What are solutions to cos⁡θ=−12\cos \theta = -\frac{1}{2} for 0∘≤θ≤360∘0^\circ \leq \theta \leq 360^\circ?

120∘,240∘120^\circ, 240^\circ

For cos⁡(2x)=0.2\cos(2x) = 0.2 with 0≤x≤3600 \leq x \leq 360, what are the limits for 2x2x?

0≤2x≤7200 \leq 2x \leq 720

When solving cos⁡(2x)=0.2\cos(2x) = 0.2, when should you divide by 2?

After finding all solutions for 2x2x

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

θ=tan⁡−1(k)+180∘n\theta = \tan^{-1}(k) + 180^\circ n

In which quadrants is sin⁡θ\sin \theta negative?

Third and fourth quadrants

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