Question

use an identity to find the value of the expression. do not use a calculator.

\\( \sin 44 ^ { \circ } \csc 44 ^ { \circ } \\)

\\( \sin 44 ^ { \circ } \csc 44 ^ { \circ } = \square \\) (type an exact answer. simplify your answer.)

Explanation:

Step1: Recall the reciprocal identity for cosecant

The reciprocal identity for cosecant is \( \csc\theta=\frac{1}{\sin\theta} \) for \( \sin\theta
eq0 \).

Step2: Substitute the identity into the expression

Substitute \( \csc44^{\circ}=\frac{1}{\sin44^{\circ}} \) into \( \sin44^{\circ}\csc44^{\circ} \), we get \( \sin44^{\circ}\times\frac{1}{\sin44^{\circ}} \).

Step3: Simplify the expression

The \( \sin44^{\circ} \) in the numerator and denominator cancels out, leaving \( 1 \).

Answer:

\( 1 \)