Mathematics

Problem

For an angle

\theta

in standard position, it is given that

\tan\theta=\tfrac34

and

\theta

lies in Quadrant III. a. (i) Find the exact values of

\sin\theta

and

\cos\theta

. b. (ii) Write the coordinates of the point on the unit circle that corresponds to

\theta

. c. (iii) List all angles

\phi

in the interval

0\le \phi<2\pi

having the same sine value as

\theta

, and write the coordinates of their corresponding points on the unit circle. d. (iv) Show algebraically that each of the points obtained in part (iii) satisfies the equation

x^{2}+y^{2}=1

. Explain the result.

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