Mathematics

Problem

Answer the following questions about the signs of trigonometric functions. a. (a) Define

\sin\theta

and

\cos\theta

with reference to the unit circle. b. (b) Using these definitions, explain why the sign of

\sin\theta

depends on the

y

–coordinate of the point on the circle. c. (c) Justify, without numerical calculation, which of the six trigonometric ratios are positive and which are negative when

180^{\circ}<\theta<270^{\circ}

. d. (d) Verify your conclusion by choosing

\theta=225^{\circ}

and computing all six ratios.

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