Let be an angle such that and .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let θ\theta be an angle such that cos⁡θ=−32\cos\theta=-\dfrac{\sqrt3}{2} and 180∘<θ<360∘180^{\circ}<\theta<360^{\circ}. (i) Identify the possible quadrants in which θ\theta can lie and state the corresponding sign of sin⁡θ\sin\theta in each. (ii) Determine the correct value of sin⁡θ\sin\theta. (iii) Write the least positive value of θ\theta satisfying the given condition in both degree and radian measure. (iv) Using the obtained values of sin⁡θ\sin\theta and cos⁡θ\cos\theta, show that sin⁡2θ+cos⁡2θ=1\sin^2\theta+\cos^2\theta=1.

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