Question

assume that θ is an acute angle in a right triangle satisfying the given condition. evaluate the remaining trigonometric functions. sin θ = 3/8 cos θ = √55/8 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) tan θ = 3√55/55 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) csc θ = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall reciprocal identity

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

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

Given $\sin\theta = \frac{3}{8}$, then $\csc\theta=\frac{1}{\frac{3}{8}}=\frac{8}{3}$.

Answer:

$\frac{8}{3}$