Question

Sketch the following in standard position.

Determine the quadrant the angle lies in (if it is on an axis, state which axis it is on and if it is + or - axis)
Then determine the reference angle.​

Answer 1

Answer: 1) Quadrant: I, reference angle:
`(2\pi)/(5)`

2) Quadrant: III, reference angle: 85°

3) Quadrant: IV, reference angle:
`(\pi)/(4)`

Explanation:

Reference angle is the angle closest to the x-axis

1) The given angle is (2/5)π. The first quadrantal (π/2) would be (2.5/5)π

Since (2/5)π < (2.5/5)π then it must be in Quadrant 1.

The angle closest to the x-axis is the same as the given angle.

2) The given angle is -95°. It is measured clockwise since it is a negative angle. Since it is greater than 90°, it is greater than the 270° quadrantal. So it must be in Quadrant III.

The angle closest to the x-axis is 85°.

3) The given angle is (23/4)π. Since (8/4)π is one rotation, this is greater than one rotation. (23/4)π - (8/4)π - (8/4)π = (7/4)π. So, it rotates two complete rotations and lands at coterminal angle (7/4)π.

The angle closest to the x-axis is π/4