Question

given tan theta=3/√(7) and sec theta < 0, find sin theta and cos theta a. sin theta= 3/4 cos theta= -√(7)/4 b. sin theta=3 cos theta=-√(7) c. sin the-3/4 cos theta=√(7)/4 sin theta=-3/4 cos theta= -√(7)/4

Answer 1

you need h for the rest and that is by pythagoras
get
\[h=\sqrt{3^2+\sqrt{7}^2}=\sqrt{9+7}=\sqrt{16}=4\]

Answer 2

also keep in mind that tangent is positive but cosine is negative (because secant is) so you must be in quadrant IV

Answer 3

therefore
\[\sin(\theta)=-\frac{3}{4}\] etc