## How to Write Each Measure in Radians

Angle measurement in geometry is represented by both a degree and a radian. $$2π$$ or $$360°$$ can be used to symbolize an entire counterclockwise rotation. As a result, degree and radian may be compared as follows:

$$2π \ = \ 360°$$ And $$π \ = \ 180°$$

In general geometry, we often represent the angle in degree ($$°$$). When measuring the angles of trigonometric or periodic functions, radians are often considered. Radians are always expressed in terms of $$pi$$: $$pi \ = \ \frac{22}{7}$$ or $$3.14$$.

### How to Convert Degrees to Radians?

$$π$$ radians is equivalent to $$180$$ degrees. Any given angle must be multiplied by $$\frac{π}{180}$$ to be converted from the degree scale to the radian scale.

Angle in radian $$=$$ Angle in degree $$\times \frac{π}{180}$$

where $$π \ = \ \frac{22}{7}$$ or $$3.14$$.

### Example

Convert $$50°$$ to radians

Solution

Angle in radian $$=$$ Angle in degree $$\times \frac{π}{180}$$ $$⇒ \ 50° \ \times \frac{π}{180} \ = \ \frac{5π}{18}$$

### Exercises for Writing Each Measure in Radians

1) Find the answer: $$440° \ =$$

2) Find the answer: $$145° \ =$$

3) Find the answer: $$-250° \ =$$

4) Find the answer: $$560° \ =$$

5) Find the answer: $$750° \ =$$

6) Find the answer: $$590° \ =$$

7) Find the answer: $$115° \ =$$

8) Find the answer: $$85° \ =$$

9) Find the answer: $$-1050° \ =$$

10) Find the answer: $$-280° \ =$$

1) Find the answer: $$440° \ =$$

$$\color{red}{\frac{440°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{440° \times 2π}{360°} \ ⇒ \ θ \ = \ \frac{22π}{9}}$$

2) Find the answer: $$145° \ =$$

$$\color{red}{\frac{145°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{145° \times 2π}{360°} \ ⇒ \ θ \ = \ \frac{29π}{36}}$$

3) Find the answer: $$-250° \ =$$

$$\color{red}{\frac{-250°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{-250° \times 2π}{360°} \ ⇒ \ θ \ = \ -\frac{25π}{18}}$$

4) Find the answer: $$560° \ =$$

$$\color{red}{\frac{560°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{560° \times 2π}{360°} \ ⇒ \ θ \ = \ \frac{28π}{9}}$$

5) Find the answer: $$750° \ =$$

$$\color{red}{\frac{750°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{750° \times 2π}{360°} \ ⇒ \ θ \ = \ \frac{25π}{6}}$$

6) Find the answer: $$590° \ =$$

$$\color{red}{\frac{750°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{750° \times 2π}{360°} \ ⇒ \ θ \ = \ \frac{59π}{18}}$$

7) Find the answer: $$115° \ =$$

$$\color{red}{\frac{115°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{115° \times 2π}{360°} \ ⇒ \ θ \ = \ \frac{23π}{36}}$$

8) Find the answer: $$85° \ =$$

$$\color{red}{\frac{115°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{115° \times 2π}{360°} \ ⇒ \ θ \ = \ \frac{17π}{36}}$$

9) Find the answer: $$-1050° \ =$$

$$\color{red}{\frac{-1050°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{-1050° \times 2π}{360°} \ ⇒ \ θ \ = \ -\frac{35π}{6}}$$

10) Find the answer: $$-280° \ =$$

$$\color{red}{\frac{-280°}{360°} \ = \ \frac{θ}{2π} \ ⇒ \ θ \ = \ \frac{-280° \times 2π}{360°} \ ⇒ \ θ \ = \ -\frac{14π}{9}}$$

## Writing Each Measure in Radians Practice Quiz

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