Question

1.) explain how to find the reference angle for 1863° and find the reference angle 2.) draw a representation of the given angle

Answer 1

Step 1. The angle that we have is:

`\begin{gathered} angle \\ a=1,863 \end{gathered}`

And we need to find the reference angle and make a representation of it.

The reference angle is always between 0° and 90° and it represents the angle between the x-axis and the terminal point of the angle.

For example

Step 2. Since we have a large angle of more than 360°, this angle will turn around the plane many times. The first step is to divide 1,863 by 360 to find the number of times that the angle will turn around the plane:

`1863/360=5.175`

The angle will complete 5 whole turns around the plane,

Step 3. Since

`360*5=1,800`

There will still be

`1,863-1800=\boxed{63}`

63 degrees left, since this angle is already between 0° and 90°, this will be the reference angle.

Step 4. 63° is the leftover angle after 5 complete turns around the plane, this will be the reference angle:

`\begin{gathered} Reference\text{ angle:} \\ 63\text{ degrees} \end{gathered}`

Step 5. The drawing representation will look as follows:

Answer:

1. Reference angle: 63°

2. The diagram is shown in step 5.