Question

Pleaseee help!!!!!!!!!!!

Angle θ lies in the fourth quadrant, and cot θ = -8/15
sin θ =
cos θ =

Answer 1

sin(θ)=−15/17
cos(θ)=8/17

Answer 2

Sin θ =
`(-15)/(17)` and
`(8)/(17)`.

Explanation:

Given : cot θ = -8/15.

To find : sin θ and cos θ.

Solution : We have given

cot θ =
`(-8)/(15)`.

cot θ =
`(adjacent)/(opposite)`.

`(adjacent)/(opposite)` =
`(8)/(-15)`.

Hypotenuse =
`\sqrt{opposite^(2) +adjacent^(2) }`

Hypotenuse =
`\sqrt{(-15)^(2) + (8)^(2) }` .

Hypotenuse =
`√(225 + 64 )` .

Hypotenuse =
`√(289 )` .

Hypotenuse =17 .

Sin θ =
`(opposite)/(Hypotenuse)`.

Plugging the values.

Sin θ =
`(-15)/(17)`.

Cos θ =
`(adjacent)/(Hypotenuse)`.

Cos θ =
`(8)/(17)`.

Therefore, Sin θ =
`(-15)/(17)` and
`(8)/(17)`.