Question

the point given below is on the terminal side of an angle θ. find the exact value of each of the six trigonometric functions of θ. (-24, 7) sin θ = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Explanation:

Step1: Calculate the radius $r$

Given the point $(x,y)=(-24,7)$, use the formula $r = \sqrt{x^{2}+y^{2}}$. So, $r=\sqrt{(-24)^{2}+7^{2}}=\sqrt{576 + 49}=\sqrt{625}=25$.

Step2: Calculate $\sin\theta$

The formula for $\sin\theta$ is $\sin\theta=\frac{y}{r}$. Substitute $y = 7$ and $r=25$ into the formula. So, $\sin\theta=\frac{7}{25}$.

Answer:

$\frac{7}{25}$