Answer:
Part 1) [tex]sin(\theta)=\frac{\sqrt{10}}{10}[/tex]
Part 2) [tex]cos(\theta)=-3\frac{\sqrt{10}}{10}[/tex]
Part 3) [tex]tan(\theta)=-1/3[/tex]
Step-by-step 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
[tex]r^{2}=x^{2} +y^{2}[/tex]
substitute the given values
[tex]r^{2}=(-3)^{2} +(1)^{2}[/tex]
[tex]r^{2}=10[/tex]
[tex]r=\sqrt{10}\ units[/tex]
step 2
Find the value of [tex]sin(\theta)[/tex]
[tex]sin(\theta)=y/r[/tex]
substitute values
[tex]sin(\theta)=1/\sqrt{10}[/tex]
Simplify
[tex]sin(\theta)=\frac{\sqrt{10}}{10}[/tex]
step 3
Find the value of [tex]cos(\theta)[/tex]
[tex]cos(\theta)=x/r[/tex]
substitute values
[tex]cos(\theta)=-3/\sqrt{10}[/tex]
Simplify
[tex]cos(\theta)=-3\frac{\sqrt{10}}{10}[/tex]
step 4
Find the value of [tex]tan(\theta)[/tex]
[tex]tan(\theta)=y/x[/tex]
substitute values
[tex]tan(\theta)=-1/3[/tex]
