Question

(10.02)

The point (−3, 1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

Answer 1

Part 1)
`sin(\theta)=(√(10))/(10)`

Part 2)
`cos(\theta)=-3(√(10))/(10)`

Part 3)
`tan(\theta)=-1/3`

Explanation:

we know that

The angle is in the second quadrant so the sine is positive, the cosine is negative and the tangent is negative

step 1

Find the radius r applying the Pythagoras theorem

`r^(2)=x^(2) +y^(2)`

substitute the given values

`r^(2)=(-3)^(2) +(1)^(2)`

`r^(2)=10`

`r=√(10)\ units`

step 2

Find the value of
`sin(\theta)`

`sin(\theta)=y/r`

substitute values

`sin(\theta)=1/√(10)`

Simplify

`sin(\theta)=(√(10))/(10)`

step 3

Find the value of
`cos(\theta)`

`cos(\theta)=x/r`

substitute values

`cos(\theta)=-3/√(10)`

Simplify

`cos(\theta)=-3(√(10))/(10)`

step 4

Find the value of
`tan(\theta)`

`tan(\theta)=y/x`

substitute values

`tan(\theta)=-1/3`