Consider the point that lies on the unit circle.

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

Problem

Consider the point P ⁣(−35,  45)P\!\left(-\dfrac35,\;\dfrac45\right) that lies on the unit circle. (i) Identify the quadrant in which the terminal side of the corresponding angle lies and justify your answer. (ii) State the values of sin⁡θ\sin \theta and cos⁡θ\cos \theta for the angle θ\theta represented by PP. (iii) Determine the signs (positive or negative) of tan⁡θ,  cot⁡θ,  sec⁡θ\tan \theta,\;\cot \theta,\;\sec \theta and csc⁡θ\csc \theta without calculating their exact numerical values. (iv) Using only the coordinates of PP, verify that sin⁡2 ⁣θ+cos⁡2 ⁣θ=1\sin^{2}\!\theta+\cos^{2}\!\theta=1. Explain why this verification is always true for any point on the unit circle.

Related theory

Browse the problem library