Question

sketch an angle θ in standard position such that θ has the least possible positive measure and the point (6,8) is on the terminal side of θ. then find the exact values of the six trigonometric functions for θ. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. sin θ = \frac{4}{5} (simplify your answer. type an integer or a fraction.) b. the function is undefined. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. cos θ = \frac{3}{5} (simplify your answer. type an integer or a fraction.) b. the function is undefined. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. tan θ = \frac{4}{3} (simplify your answer. type an integer or a fraction.) b. the function is undefined. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. csc θ = \square (simplify your answer. type an integer or a fraction.) b. the function is undefined.

Explanation:

Step1: Recall reciprocal identity of sine and cosecant

The cosecant function is the reciprocal of the sine function, i.e., $\csc\theta=\frac{1}{\sin\theta}$.

Step2: Substitute the value of $\sin\theta$

We know from the problem that $\sin\theta = \frac{4}{5}$. Substituting this into the reciprocal identity, we get $\csc\theta=\frac{1}{\frac{4}{5}}$.

Step3: Simplify the fraction

To divide by a fraction, we multiply by its reciprocal. So $\frac{1}{\frac{4}{5}} = 1\times\frac{5}{4}=\frac{5}{4}$.

Answer:

$\frac{5}{4}$