Answer the following questions about the signs of trigonometric functions.

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

Problem

Answer the following questions about the signs of trigonometric functions. (a) Define sin⁡θ\sin\theta and cos⁡θ\cos\theta with reference to the unit circle. (b) Using these definitions, explain why the sign of sin⁡θ\sin\theta depends on the yy–coordinate of the point on the circle. (c) Justify, without numerical calculation, which of the six trigonometric ratios are positive and which are negative when 180∘<θ<270∘180^{\circ}<\theta<270^{\circ}. (d) Verify your conclusion by choosing θ=225∘\theta=225^{\circ} and computing all six ratios.

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