Answer:
Explanation:
First of all, we know that
[tex]\sin \frac{\pi}{4}=\frac{\sqrt[]{2}}{2}[/tex]And knowing the unit circle, we know that the sine takes negative values in 3rd and 4th quadrants. Therefore, from the above value of the angle, If we go π radians counterclockwise, we encounter negative values of sine; hence,
[tex]\sin \lbrack\frac{\pi}{4}+\pi\rbrack=-\frac{\sqrt[]{2}}{2}[/tex][tex]\rightarrow\sin \frac{5\pi}{4}=\frac{-\sqrt[]{2}}{2}[/tex]The second value of the angle that yields the above value for sine is found by adding π/2 radians to the angle above (we are now in the 4th quadrant)
[tex]\sin \frac{5\pi}{4}+\frac{\pi}{2}=-\frac{\sqrt[]{2}}{2}[/tex][tex]\rightarrow\sin \frac{7\pi}{4}=-\frac{\sqrt[]{2}}{2}[/tex]Hence, the two values of angles between 0 and 2π are 5π/4 and 7π/4.
