Question

if $sin\theta=\frac{11}{12}$, find $csc\theta$.
$csc\theta=square$

Explanation:

Step1: Recall the reciprocal identity

The reciprocal identity for cosecant and sine is \(\csc\theta=\frac{1}{\sin\theta}\).

Step2: Substitute the given value of \(\sin\theta\)

Given \(\sin\theta = \frac{11}{12}\), then \(\csc\theta=\frac{1}{\frac{11}{12}}\).

Step3: Simplify the expression

When dividing by a fraction, we multiply by its reciprocal. So \(\frac{1}{\frac{11}{12}}=1\times\frac{12}{11}=\frac{12}{11}\).

Answer:

\(\frac{12}{11}\)