Question

1. a) choose an angle between 90° and 180°. sketch a diagram to show that the angle can be formed by reflecting its reference angle in an axis or axes.

180 - 120° = 60°
b) repeat part a for an angle between 180° and 270°.
c) repeat part a for an angle between 270° and 360°.

Explanation:

Step1: Choose an angle for part a

Let's choose \(120^{\circ}\). The reference angle \(\theta_{r}=180 - 120=60^{\circ}\). To form \(120^{\circ}\) from its reference angle \(60^{\circ}\), we reflect the reference angle (in the first - quadrant) over the \(y\) - axis.

Step2: Choose an angle for part b

Let's choose \(210^{\circ}\). The reference angle \(\theta_{r}=210 - 180 = 30^{\circ}\). To form \(210^{\circ}\) from its reference angle \(30^{\circ}\), we reflect the reference angle (in the first - quadrant) over the \(x\) - axis and then over the origin (or equivalently, reflect over the \(x\) - axis and then add \(180^{\circ}\)).

Step3: Choose an angle for part c

Let's choose \(330^{\circ}\). The reference angle \(\theta_{r}=360 - 330=30^{\circ}\). To form \(330^{\circ}\) from its reference angle \(30^{\circ}\), we reflect the reference angle (in the first - quadrant) over the \(x\) - axis.

Answer:

a) For \(120^{\circ}\) (reference angle \(60^{\circ}\)), reflect \(60^{\circ}\) (in the first quadrant) over the \(y\) - axis.
b) For \(210^{\circ}\) (reference angle \(30^{\circ}\)), reflect \(30^{\circ}\) (in the first quadrant) over the \(x\) - axis and then consider the angle in the third quadrant (or reflect over the \(x\) - axis and then add \(180^{\circ}\)).
c) For \(330^{\circ}\) (reference angle \(30^{\circ}\)), reflect \(30^{\circ}\) (in the first quadrant) over the \(x\) - axis.