`(-4, 10)` The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.

Textbook Question

Chapter 4, 4.4 - Problem 16 - Precalculus (3rd Edition, Ron Larson).
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kspcr111 | In Training Educator

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Given the point on the terminal (x,y) = (-4,10)

so,

x= -4, y= 10 

then `r=sqrt((-4)^2+(-10)^2) =sqrt(16+100) =sqrt(116)`

then 

let ` theta`  be the angle

then

`sin theta = y/r = 10/sqrt(116)`

`cos theta =x/r = -4/sqrt(116)`

`tan theta = y/x = 10/-4 = -10/4`

`csc theta = r/y = sqrt(29)/10 = sqrt(116)/10`

`sec theta = r/x =sqrt(29)/-4 = -sqrt(116)/4`

`cot theta = x/y = -4/10`

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