Find the values of six trigonometric functions of theta with

Find the values of six trigonometric functions of theta with given constraint tan theta = -15/8, Constraint: theta lies in Quadrant II.

Solution

tan theta=-15/8            theta lies in second quadrant

Here opposite=15   and adjacent=8

hypotenuse=sqrt(15²+8²) = 17

sine is positive in seond quadrant and cosine is negative

sin theta=opposite/hypotenuse= 15/17

cos theta=adjacent/hypotenuse = -8/17

cosec theta=1/sin theta= 17/15

sec theta=1/cos theta= -17/8

cot theta=1/tan theta= -8/15