find the exact value of cos theta tan theta103 theta in quad

find the exact value of cos theta. tan theta=-10/3, theta in quadrant II

Solution

tan theta=-10/3   thetais in second quadrant and in second quadrant,cos theta is negative

Here opposite= 10 and adjacent=3

hypotenuse= sqrt(100+9)=sqrt109

cos theta= adjacent/hypotenuse= - 3/sqrt109= -3sqrt109/109