# Converting angle units (degree, radian, revolution) – problems and solutions

1. ¼ rev = ….. ^{o} (degree) ?

Solution

1 rev = 360^{o}

½ rev = 180^{o}

¼ rev = 90^{o}

2. ½ rev = …….. rad ?

Solution

1 rev = 2π rad = 2(3.14) rad = 6.28 rad

½ rev = pi rad = 3.14 rad

3. 180^{o} = ….. rev ?

Solution

360^{o} = 1 rev

180^{o} = ½ rev

4. 90^{o} = ….. rad ?

Solution

360^{o} = 2π rad = 2(3.14) rad = 6.28 rad

180^{o} = π rad = 3.14 rad

90^{o} = ½ π rad = ½ (3.14) = 1.57

5. 60 rad = ….. rev ?

Solution

6.28 rad = 1 rev

60 rad/6.28 = 9.55 rev

6. 40 rad= ….. ^{o} ?

Solution

6.28 rad = 360^{o}

40 rad/6.28 = (6.37)(360^{o}) = 2292.99^{o}

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