Express the following angles in radians: (a)20.0°,(b)50.0°,100°Convert the following angles to degrees:(d)0.330rad,(e)2.10rad,(f)7.70rad

Short Answer

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a)Anglesinradians;20.0°=0.349rad50.0°=0.873rad100.0°=1.75radb) Anglesindegrees:0.330rad=18.9°0.330rad=120°0.330rad=441°

Step by step solution

01

Understanding the relation between degree and radian.

360°of2πradof makes up a complete circle angle. This means a circle subtends an angle with radian 2πand degree 360° at its centre. An angle's measure can be converted from one unit to another based on the following formula.

360°=2πrad(1)Givenaretheanglesindegrees20°,50°,100°andAnglesinradians0.330rad.2.10rad,7.70rad.

02

To calculate angle in radians part a)

Using equation (i) the angle can be expressed in radians as

20.0°=((20.0°)2π360°rad=0.349rad50.0°=((50.0°)2π360°rad=0.873rad100.0°=((100.0°)2π360°rad=1.75rad

03

To calculate angle in degrees part b)

Using equation (i) the angle can be expressed in degrees as

0.330rad=(0.330rad)360°2πrad=18.9°2.10rad=(2.10rad)360°2πrad=120°7.70rad=(7.70rad)360°2πrad=441°

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