Question

(a) If θ is in standard position, then the reference angle θ is the acute angle formed by the terminal side of θ and the . So the reference angle for θ = 110° is θ = °, and that for θ = 210° is θ =

Answer 1

In mathematics, a reference angle is the acute angle formed by the terminal side of a given angle and the x-axis, used for angles in standard position. The reference angle for θ = 110° is 70° and for θ = 210° it is 30°.

Step-by-step explanation:

The concept of reference angles is often taught in mathematics, particularly in trigonometry to help understand the properties of angles in different quadrants of the Cartesian plane. A reference angle is always the acute angle (less than 90°) that the terminal side of the given angle makes with the x-axis. In standard position, the reference angle for an angle is the smallest angle between the terminal side of the angle and the horizontal axis (x-axis).

For an angle θ of 110°, which lies in the second quadrant, the reference angle would be 180° - 110° = 70°. Similarly, for an angle θ of 210° that lies in the third quadrant, the reference angle is calculated as 210° - 180° = 30°. Thus, the reference angle for θ = 110° is 70°, and for θ = 210°, it is 30°.

Answer 2

70 degree, 30 degree

Step-by-step explanation:

We are given that
`\theta` is in standard position.

The reference angle
`\theta` is the acute angle.

Acute angle :The angle is always less than 90 degree.

The reference angle formed by terminal side of angle
`\theta` with x-axis.

When
`\theta=110^(\circ)`

Then, the reference angle =
`\bar{\theta}=180-110`

`\bar{\theta}=70^(\circ)`

When
`\theta=210^(\circ)`

Therefore, the reference angle

`\bar{\theta}=210-180`

`\bar{\theta}=30^(\circ)`