Answer:
Explanation:
You want to convert 45 degrees to radians and vice versa.
Angle measures
A full circle consists of 2π radians, or 360°. Another measure sometimes used for angles is gradians (grads), of which 400 make a circle.
In astronomy and celestial navigation, angles of relative longitude are measured in hours, with 24 hours making a full circle.
All angle measures are proportional to one another, so can be converted using appropriate scale factors.
360° = 2π rad = 400 gon = 24 h
45°
Since there are 2π radians in 360°, π radians corresponds to 180°. To convert 45° to radians, you can multiply by π/180 (radians per degree).
45° = 45° × π/180° = π(45/180) = π/4 . . . . radians
In the reverse direction, the inverse multiplier is used:
π/4 = π/4 × 180°/π = 180°/4 = 45°
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Additional comment
A radian is a dimensionless unit. 1 rad = 1 (a pure number with no units). Often, in mathematical writing, the "rad" is omitted.
A radian is the measure of the central angle of a sector that has an arc length equal to its radius. It is about 57.29578°, very close to 57 21/71°.