Question

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assume that θ is an acute angle in a right - triangle satisfying the given condition. evaluate the remaining trigonometric functions.
cosθ = 5/13
sinθ = 12/13 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
tanθ = 12/5 (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
cscθ = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the reciprocal relationship of cosecant and sine

The formula is $\csc\theta=\frac{1}{\sin\theta}$.

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

Since $\sin\theta = \frac{12}{13}$, then $\csc\theta=\frac{1}{\frac{12}{13}}$.

Step3: Simplify the expression

$\frac{1}{\frac{12}{13}}=\frac{13}{12}$.

Answer:

$\frac{13}{12}$