Answer:
To find the reference angle and the quadrant of,
[tex]675\degree[/tex]
we have that,
Every angle is measured from the positive part of the x-axis to its terminal line traveling counterclockwise. If you want to find the reference angle, you have to find the smallest possible angle formed by the x-axis and the terminal line, going either clockwise or counterclockwise. If you want to find the reference angle, you have to find the smallest possible angle formed by the x-axis and the terminal line, going either clockwise or counterclockwise.
Since we get that,
The angle 675 degrees lies between (2x270=) 540 degrees and (2x360=) 720 degrees,
Therefore, the angle lies in the fourth quadrant.
To find the reference angle:
we get,
Reference angle is,
[tex]2\times360\degree-r=675\degree[/tex]
where r is the reference angle.
Solving the above equation we get,
[tex]720\degree-r=675\degree[/tex][tex]r=720\degree-675\degree[/tex][tex]r=45\degree[/tex]
The reference angle is 45 degrees and it lies in 4th quadrant.
