Question

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

sin(θ) =

cos(θ) =

tan(θ) =

csc(θ) =

sec(θ) =

cot(θ) =

Answer 1

Explanation:

Alright, lets get started.

Please refer the diagram I have attached.

The point (8, -15) shows it is in 4th quadrant.

side X is 8 and side Y is -15.

We can find side R with help of Pythagorean theorem.

`R^2=8^2+(-15)^(2)=289`

Taking square root,

`R = 17`

sinΘ=
`(Y)/(R)=(-15)/(17)`

cosΘ=
`(X)/(R)=(8)/(17)`

tanΘ=
`(X)/(Y)=(-15)/(8)`

cscΘ=
`(R)/(X)=(17)/(-15)=-(17)/(15)`

secΘ=
`(R)/(X)=(17)/(8)`

cotΘ=
`(X)/(Y)=(8)/(-15)=-(8)/(15)`

Answer

Hope it will help :)