Question

Find the exact value of s in the given interval that has the given circular function value.

Answer 1

Answer:

$\displaystyle s=\frac{3\pi}{4}$

Step-by-step explanation:

Trigonometric Values

We need to find the angle s in the interval [π/2,π] where:

$\displaystyle \sin s=\frac{\sqrt{2}}{2}$

There are two possible angles that have the same sine value in the first rotation of s. Any angle on the first quadrant has the same sine as its supplementary angle in the second quadrant.

The first angle s whose sine is $\frac{\sqrt{2}}{2}$ is:

$\displaystyle s=\frac{\pi }{4}$

The other angle is its supplementary angle:

$\displaystyle s=\pi-\frac{\pi }{4}=\frac{3\pi}{4}$

Only this last angle lies on the required interval, thus:

$\boxed{\displaystyle s=\frac{3\pi}{4}}$