Answer:
[tex]\frac{\sqrt{731}}{30}[/tex]
Step-by-step explanation:
We first observe that the angle is located in quadrant III
This allows us to draw a triangle as attached in the attachments.
Using this triangle, we can find sin([tex]\theta_1[/tex]).
Remembering that sin(theta) = [tex]\frac{opp}{hypo}[/tex], we can see from the attached image that it is [tex]\frac{\sqrt{30^2 - 13^2}}{30}[/tex], then simplifying [tex]\sqrt{30^2 - 13^2}[/tex] using a calculator, we get [tex]\sqrt{731}[/tex].
So our final answer is the answer shown above.
You may be wondering how did the side lengths appear on the triangle.
From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.
