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Convert the angle into radians. Then draw it in standard position.

[tex]\[ \theta = 210^\circ \][/tex]


Sagot :

To convert an angle from degrees to radians, you can use the following relationship:

[tex]\[ \text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180} \right) \][/tex]

Given an angle of 210°, we can follow these steps:

1. Identify the given angle in degrees:
The given angle is 210°.

2. Convert degrees to radians:
To convert degrees to radians, multiply the degree measure by [tex]\(\frac{\pi}{180}\)[/tex]:
[tex]\[ 210^\circ \times \left( \frac{\pi}{180} \right) \][/tex]

3. Carry out the multiplication:
Simplify the fraction and calculate the radian measure:
[tex]\[ 210^\circ \times \left( \frac{\pi}{180} \right) = \frac{210\pi}{180} = \frac{21\pi}{18} = \frac{7\pi}{6} \][/tex]

So, the angle in radians is:
[tex]\[ \frac{7\pi}{6} \approx 3.6651914291880923 \][/tex]

Next, let's draw the angle of 210° in standard position:

1. Draw the coordinate system:
Draw the x-axis (horizontal line) and y-axis (vertical line) intersecting at the origin (0,0).

2. Identify the initial side:
The initial side of the angle in standard position lies along the positive x-axis.

3. Rotate the initial side counterclockwise:
Rotate the initial side counterclockwise until it reaches 210°. Since 210° is greater than 180°, the terminal side will also be in the third quadrant (between 180° and 270°).

4. Place the terminal side:
Mark the terminal side 30° past the -x axis (since 210° - 180° = 30°). This means the terminal side of the angle lies in the third quadrant.

The final diagram will show the initial side along the positive x-axis and the terminal side extending into the third quadrant, creating an angle of 210° measured counterclockwise from the positive x-axis.