Suppose that sec t equals 133 and that it is in quadrant 2 F

Suppose that sec (t) equals -13/3 and that it is in quadrant 2. Find the exact value of tan (t).

Solution

sec t = -13/3

hypotenuse = 13

base = 3

perpendicular = sqrt ( 13^2 - 3^2 ) = sqrt 160 = 4 sqrt 10

tan t = perpendicular / base

= - 4 sqrt 10 / 3

tan t = - 4 sqrt 10 / 3