A point on the terminal side of an angle theta is given Find

A point on the terminal side of an angle theta is given. Find the exact value of the indicated trigonometric function. (-1, -1) Find csc theta

Solution

Point lies in the 3rd quadrant : ( -1 , -1)

The right angled triangle formed by the point , x axis , and origin :

hypoteunse = sqrt(1 +1) = sqrt2

csctheta = 1/sintheta = - 1/sqrt2    ; sin is -ve in III rd quadrant