How to Write Each Measure in Radians

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: \(-280° \ =\)

 

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