Question

find the exact value of csc 45°. csc 45° = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the definition of cosecant

The cosecant function is defined as $\csc\theta=\frac{1}{\sin\theta}$. So, $\csc45^{\circ}=\frac{1}{\sin45^{\circ}}$.

Step2: Find the value of $\sin45^{\circ}$

We know that $\sin45^{\circ}=\frac{\sqrt{2}}{2}$.

Step3: Calculate $\csc45^{\circ}$

Substitute $\sin45^{\circ}=\frac{\sqrt{2}}{2}$ into the formula for $\csc45^{\circ}$. Then $\csc45^{\circ}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}$. Rationalize the denominator: $\frac{2}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\sqrt{2}$.

Answer:

$\sqrt{2}$