The terminal side of angle β in standard position goes through the point (-15,-8). Find the values of the six trigonometric functions of β.

Answer 1

The point is (-15, -8). It is in the third quadrant.

We can readily calculate tan β and cot β:

tan β = y/x = -8/-15 = 8/15

cot β = 1/tan β = 15/8

For the rest we need the hypothenuse. The hypotenuse is calculated by

h = sqrt(x^2 + y^2)

h = sqrt((-15)^2+ (-8)^2)

h = sqrt(225 + 64)

h = sqrt(289)

h = 17

cos β = x / h = -15/17

sec β = 1 / cos β = -17/15

sin β = y / h = -8/17

csc β = 1 / sin β = -17/8

Answer 2

(-15,-8) is in quadrant 3 where all trig functions<0 except tan & cot

use the pythagorean theorem

hypotenuse of the reference angle = square root of (225 + 64) =sqr289=17

opposite side= -8, adjacent side=-15

tangent=opposite side over adjacent side

sine = opposite side over hypotenuse

cosine = adjacent side over hypotenuse

tanB = 8/15

cotB= 1/tanB=15/8

sinB =-8/17

cscB = 1/sinB=-17/8

cosB =-15/17

secB =1/cosB=-17/15