Question

if theta is in second quadrant and 3tan theta+4=0, find 15sin theta+10 cos theta - 8 cot theta

Answer 1

$3 \tan( \alpha ) + 4 = 0 \\ \tan( \alpha ) = - \frac{4}{3} \\ \cot( \alpha ) = \frac{ - 3}{4} \\ \sin( \alpha ) = \frac{4}{5} \\ \cos( \alpha ) = \frac{ - 3}{5} \\ 15 \sin( \alpha ) + 10 \cos( \alpha ) - 8 \cot( \alpha ) \\ = 15 \times \frac{4}{5} + 10 \times \frac{ - 3}{5} - 8 \times \frac{ - 3}{4} \\ = 12 - 6 + 6 \\ = 12$