Answer the following with reference to angles in the first quadrant.

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

Problem

Answer the following with reference to angles in the first quadrant. (a) Define the unit circle and state how the coordinates of a point on it are related to sin⁡θ\sin \theta and cos⁡θ\cos \theta for an angle θ\theta. (b) Complete the following table by writing the exact values (in simplest rationalised radical form) of sin⁡θ\sin \theta and cos⁡θ\cos \theta for θ=0∘, 30∘, 45∘, 60∘, 90∘\theta = 0^{\circ},\,30^{\circ},\,45^{\circ},\,60^{\circ},\,90^{\circ}. (c) For each of the above angles, write the corresponding coordinate pair (cos⁡θ, sin⁡θ)(\cos \theta,\,\sin \theta) on the unit circle.

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