Question

Hey guys, I'm getting two different answers with two methods that should get the same answer.
Q: Convert 90 degrees into radians

A1: Using formula theta radians = S/r, S = 1/4 because 90 degrees cuts the circle into fourths. Then I said radius is 1 because it doesn't matter what the radius size is, the ratio will always be the same. Then, I get theta radians = 1/4. So my answer is 1/4 radians.

A2: I know 1 degree = pi/180 radians, thus 90 degrees means pi/2 radians.

I feel like A2 is right but I can't seem to grasp why A1 is wrong. I think my question is, what is my flaw in logic?

Answer 1

You're correct that 90 degrees divide the circle in 4 quadrants but the variable s in the formula is a length whereas you are only taking one-fourth as s.
Actually s would be one-fourth of the circumference of the circle so:
\[s=\frac{ 1 }{ 4 }\times2\pi r \]
since radians = s/r
\[\frac{ 2 \pi r }{ 4 }\div r = \frac{ 2 \pi }{ 4 } =\frac{ \pi }{ 2 }\]

Answer 2

Ohhh, that makes sense. Thanks so much!