The terminal side of theta lies on the given line in the spe

The terminal side of theta lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of theta by finding a point on the line. sin theta = cos theta = tan theta = csc theta = sec theta = cot theta =

Solution

3x - y = 0

in quadrant 3 both x and y are negative

so lets find a point that lies on the line by picking a value for x

let x = -1

y = 3(-1) = -3

finding hypotenuse

h^2 = (-1)^2 + (-3)^2

h = sqrt 10

sin theta = perpendicular / hypotenuse = -3/ sqrt 10 = - 3 sqrt 10/ 10

cos theta = base / hypotenuse = -1 / sqrt 10 = -sqrt 10 / 10

tan theta = perpendicular / base = -3 / -1 = 3

csc theta = 1/ sin theta = - sqrt 10 /3

sec theta = 1 / cos theta = -sqrt 10

cot theta = 1/ tan theta = 1/3