Answer:
Explanation:
The relationship between angle measures in degrees and angle measures in radians does not depend on the radius of the circle. It is always ...
180° = π radians
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Then an angle of 45° will be ...
45° × (π radians)/(180°) = π/4 radians
This value is the same for a radius of 5 cm or of 1 cm.
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Additional comment
We have made the conversion from degrees to radians using a conversion factor that has radians in the numerator and degrees in the denominator. When we mutiply by this factor, the units of degrees cancel, leaving units of radians. We use a conversion factor that has the same angle value in numerator and denominator, so it doesn't change the angle we're multiplying. It only changes the units.
The same relation can be expressed as a proportion:
(π radians)/180° = (x radians)/(45°)
When you multiply this equation by 45° on both sides, you get the equation we used above.