How to Write Each Measure in Radians

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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 $\times \frac{π}{180}$ $⇒ \ 50° \ \times \frac{π}{180} \ = \ \frac{5π}{18}$

Free printable Worksheets

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: $-280° \ =$

Answers

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: $-280° \ =$

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

How to Write Each Measure in Radians