Consider the given expression,
[tex]\sin (\frac{17\pi}{4})[/tex]
A unit circle is a circle whose radius is unity.
Make sections of 45 degrees each,
[tex]\frac{\pi}{4}=45^{\circ}[/tex]
Since sine function has a period of 360 degree.
The values will get repeated after 360+ angle measurements.
Therefore, in order to mark the given angle, we need to move anticlockwise from the positive axis and make 2 full rounds and then take one more step of 45 degrees.
Thus, it is seen that the gine of given angle is the same as sine of 45 degrees.
Mathematically,
[tex]\sin (\frac{17\pi}{4})=\sin (2\pi+2\pi+\frac{\pi}{4})=\sin (\frac{\pi}{4})=\frac{1}{\sqrt[]{2}}\approx0.707[/tex]
Thus, the value of the given expression is 0.707 approximately.
