Find the exact value of the expression. Do not use a calculator.

(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.)

Ask by Martin Rodriquez. in the United States

Jan 25,2025

Question

Find the exact value of the expression. Do not use a calculator.

(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.)

Ask by Martin Rodriquez. in the United States

Jan 25,2025

UpStudy AI · Accepted Answer

We are given the expression:

$$
\frac{\sin \left(44^{\circ}\right)}{\cos \left(46^{\circ}\right)}
$$

Notice that $$44^{\circ}$$ and $$46^{\circ}$$ are complementary angles because:

$$
44^{\circ} + 46^{\circ} = 90^{\circ}
$$

Using the cofunction identity, we know that:

$$
\sin(\theta) = \cos(90^{\circ} - \theta)
$$

Applying this to our angles:

$$
\sin(44^{\circ}) = \cos(46^{\circ})
$$

Therefore, the expression simplifies to:

$$
\frac{\sin \left(44^{\circ}\right)}{\cos \left(46^{\circ}\right)} = \frac{\cos \left(46^{\circ}\right)}{\cos \left(46^{\circ}\right)} = 1
$$

**Answer:** $$1$$
$$ \frac{\sin \left(44^{\circ}\right)}{\cos \left(46^{\circ}\right)} = 1 $$