Question

use the given triangle to evaluate the expression. if necessary, express the value without a square root in the denominator by rationalizing the denominator. sin(π/4) - sin(π/4) sin(π/4) - sin(π/4) = □ (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize

Explanation:

Step1: Recall sine value of $\frac{\pi}{4}$

The sine of $\frac{\pi}{4}$ (or 45 - degrees) in a right - triangle with sides 1, 1, $\sqrt{2}$ is $\sin\frac{\pi}{4}=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}$.

Step2: Substitute into the expression

Substitute $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$ into $\sin\frac{\pi}{4}-\sin\frac{\pi}{4}$. We get $\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}$.

Step3: Calculate the result

$\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}=0$.

Answer:

$0$