find the values of all 6 trigonometric functions for the ang

Find the values of all 6 trigonometric functions for the angle defined by the given point

Solution

1. ( -2 , 1)

applying pythagorean theorem to find the length of the hypotenuse

hypotenuse = sqrt ( 2^2 + 1^2) = sqrt 5

sin theta = perpendicular / hypotenuse = 1 / sqrt 5 = sqrt 5 / 5

cos theta = base / hyp = -2 / sqrt 5 = - 2 sqrt 5 / 5

tan theta = per / base = 1 /-2 = -1/2

csc theta = 1/ sin theta = sqrt 5

sec theta =1/ cos theta = - sqrt 5 / 2

cot theta =1 / tan theta = -2

2) ( -3 , -3)

hypotenuse = sqrt ( 3^2 +3^2 ) = sqrt 18 = 3 sqrt 2

sin theta = -3 / 3 sqrt 2 = - sqrt 2 / 2

cos theta = - sqrt 2 / 2

tan theta =-3 / -3 = 1

csc theta = 1/ sin theta = - sqrt 2

sec theta = 1/ cos theta = - sqrt 2

cot theta = 1/ tan theta = 1