Thank you Complete all of the following problems Show work w

Complete all of the following problems. Show work when appropriate. Use the Basic Trigonometric Identities to evaluate the related function, If sin theta = 4/5 and pi/2

Solution

sin theta = 4/5

theta lies between pi/2 to pi that is 2nd quadrant

sin theta = perpendicular / hypotenuse

perpendicular = 4

hypotenuse = 5

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

therefore, cot theta = base / perpendicular = 3 / 4

since in 2nd quadrant cot theta is negaive therefore value is cot theta = - 3/4

2) tan x = -1

x lies in 2nd quadrant

tan x = perpendicular / base

perpendicular = 1

base = 1

hypotenuse = sqrt ( 1^2 + 1^2 ) = sqrt 2

sin x = perpendicular / hypotenuse = 1 / sqrt 2 = sqrt 2 / 2

cos x = base / hypotenuse = - 1 / sqrt 2 = - sqrt 2 / 2

sec x = 1 / cos x = - sqrt 2

cosec x = 1 / sin x = sqrt 2

cot x = 1 / tan x = -1