Write the first trigonometric functions in terms of the second for θ in the given quadrant.

Question

1) cos(θ), sin(θ); θ in Quadrant IV

2) sec(θ), tan(θ); θ in Quadrant II

Answer 1

cos(α)=b/c, sin(α)=a/c, sin/cos=tan, cos/sin=cot, sec=1/cos, csc=1/sin

1. cos(α)=b/c=tan(β)*sin(α)

or (b/c)/(b/a)=a/c=sin(α) 91°-180°

2. sec(α)=1/cos(α) or c/b. So (c/b)/(a/b)=c/a And (c/b)/(c/a)=a/b=tan(α).

270°-360°