Mathematics

Problem

Consider the point

P\!\left(-\dfrac35,\;\dfrac45\right)

that lies on the unit circle. a. (i) Identify the quadrant in which the terminal side of the corresponding angle lies and justify your answer. b. (ii) State the values of

\sin \theta

and

\cos \theta

for the angle

\theta

represented by

P

. c. (iii) Determine the signs (positive or negative) of

\tan \theta,\;\cot \theta,\;\sec \theta

and

\csc \theta

without calculating their exact numerical values. d. (iv) Using only the coordinates of

P

, verify that

\sin^{2}\!\theta+\cos^{2}\!\theta=1

. Explain why this verification is always true for any point on the unit circle.

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