Let theta be an angle such that sec theta 54 and cot theta

Let theta be an angle such that sec theta = 5/4 and cot theta

Solution

sec theta = 5/4

sec theta = hypotenuse / base

perpendicular = sqrt (5^2 - 4^2 ) = 3

cot theta < 0

therefore, theta lies in 4th quadrant since sec theta is positive and cot theta negative

tan theta = perpendicular / base = - 3 / 4

csc theta = hypotenuse / perpendicular = - 5/ 3