Question

Trigonometry Give the reference angle and the quadrant of the following

Answer 1

To find the reference angle and the quadrant of,

`675\degree`

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,

`2*360\degree-r=675\degree`

where r is the reference angle.

Solving the above equation we get,

`720\degree-r=675\degree`
`r=720\degree-675\degree`
`r=45\degree`

The reference angle is 45 degrees and it lies in 4th quadrant.