For an angle in standard position

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

For an angle θ\theta in standard position, it is given that tan⁡θ=34\tan\theta=\tfrac34 and θ\theta lies in Quadrant III. (i) Find the exact values of sin⁡θ\sin\theta and cos⁡θ\cos\theta. (ii) Write the coordinates of the point on the unit circle that corresponds to θ\theta. (iii) List all angles ϕ\phi in the interval 0≤ϕ<2π0\le \phi<2\pi having the same sine value as θ\theta, and write the coordinates of their corresponding points on the unit circle. (iv) Show algebraically that each of the points obtained in part (iii) satisfies the equation x2+y2=1x^{2}+y^{2}=1. Explain the result.

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