A ray starting from the positive –axis is rotated clockwise through to reach a point…

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

Problem

A ray starting from the positive xx–axis is rotated clockwise through 135∘135^{\circ} to reach a point PP on the unit circle. Let the angle of rotation be θ\theta (measured from the positive xx–axis in the standard position). (i) Express θ\theta in radians. (ii) Determine the coordinates of the point PP. (iii) Hence calculate sin⁡θ\sin\theta, cos⁡θ\cos\theta, tan⁡θ\tan\theta, sec⁡θ\sec\theta, csc⁡θ\csc\theta and cot⁡θ\cot\theta. (iv) Confirm numerically that tan⁡θ cot⁡θ=1\tan\theta\,\cot\theta=1 for this angle.

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