Question

watch the video and then solve the problem given below. click here to watch the video. find the exact value of each of the six trigonometric functions of θ, if (-2, -3) is a point on the terminal side of angle θ. sin θ = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Explanation:

Step1: Calculate the radius $r$

Given the point $(x,y)=(-2,-3)$, use the formula $r = \sqrt{x^{2}+y^{2}}$. So $r=\sqrt{(-2)^{2}+(-3)^{2}}=\sqrt{4 + 9}=\sqrt{13}$.

Step2: Calculate $\sin\theta$

The formula for $\sin\theta$ is $\sin\theta=\frac{y}{r}$. Substitute $y=-3$ and $r = \sqrt{13}$ into it, we get $\sin\theta=\frac{-3}{\sqrt{13}}=-\frac{3\sqrt{13}}{13}$.

Answer:

$-\frac{3\sqrt{13}}{13}$