Find the exact values of the remaining trigonometric functio

Find the exact values of the remaining trigonometric functions of theta from the given information. cos theta = - 5/13, theta in quadrant III tan theta = -3/4, theta in quadrant IV cot theta = -3/4, theta in quadrant II sec theta = 4/Squareroot 7, theta in quadrant IV sec theta = 3/5, tan theta 0 sec theta = 3, sin thet5a 0

Solution

49)

cos theta = -5/13 in quadrant 3

cos theta is given by the formula base / hypotenuse

base = 5

hypotenuse = 13

perpendicular = sqrt ( 13^2 - 5^2 ) = 12

sin theta = perpendicular / hypotenuse = - 12 / 13

tan theta = perpendicular / base = 12 / 5 ( tan is positive in quadrant 3 )

csc theta = 1/ sin theta = - 13 / 12

sec theta = 1/ cos theta = - 13 / 5

cot theta = 1/ tan theta = 5 / 12