Question

to convert an angle measure from degrees to radians, what should the angle measure be multiplied by?
a (\frac{pi}{180^{circ}})
b (\frac{180^{circ}}{pi})
c (\frac{pi}{360^{circ}})
d (\frac{360^{circ}}{pi})

Explanation:

Step1: Recall the conversion formula

We know that \(180^{\circ}=\pi\) radians. Let \(x\) be the angle in degrees. To convert \(x\) degrees to radians, we set up the proportion \(\frac{x}{1}=\frac{\text{radians}}{\frac{\pi}{180}}\).

Step2: Derive the conversion multiplier

If \(x\) (in degrees) \(\times k=\) radians, and since \(180^{\circ}\times\frac{\pi}{180}=\pi\) radians. So the multiplier \(k = \frac{\pi}{180}\)

Answer:

C. \(\frac{\pi}{180}\)