Question

Can you show how to find the solution of number 9 on a unit circle

Answer 1

Given:

`(7\pi)/(4)`

To Determine: The value of the given on a unit circle

Solution

For sin 7pi/4, the angle 7pi/4 lies between 3pi/2 and 2pi (Fourth Quadrant)

`\begin{gathered} sin((7\pi)/(4)) \\ Note:(3\pi)/(2)<(7\pi)/(4)<2\pi \\ Therefore,the\text{ angle lies in the 4th quadrant} \end{gathered}`

This is as shown below

In a simplified form, we have it as shown in the image below

`The\text{ coordinate of sin}(7\pi)/(4)=(0.7071,-0.7071),or((1)/(√(2)),-(1)/(√(2)))`

Note that sine is negative in the fourth quadrant

`\begin{gathered} sin((7\pi)/(4))=-sin(2\pi-(7\pi)/(4)) \\ sin((7\pi)/(4))=-sin((8\pi-7\pi)/(4)) \\ sin((7\pi)/(4))=-sin((\pi)/(4)) \\ sin((7\pi)/(4))=-(1)/(√(2)),or,-(√(2))/(2) \end{gathered}`

Hence,

`\begin{gathered} sin((7\pi)/(4))=-(1)/(√(2)),or \\ sin((7\pi)/(4))=-(√(2))/(2) \end{gathered}`