Question

I dont get how to solve the problem with a unit circle

Answer 1

Consider the given expression,

`\sin ((17\pi)/(4))`

A unit circle is a circle whose radius is unity.

Make sections of 45 degrees each,

`(\pi)/(4)=45^(\circ)`

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,

`\sin ((17\pi)/(4))=\sin (2\pi+2\pi+(\pi)/(4))=\sin ((\pi)/(4))=\frac{1}{\sqrt[]{2}}\approx0.707`

Thus, the value of the given expression is 0.707 approximately.