Question

What is the angle of 135 degrees equal to in radian measure?

Answer 1

Make sure you know the conversion formula

For me I always remember one thing
\[l = r \theta\]
\[When ~ l=C = 2\pi r = r \theta, ~ \theta = 2\pi = 360^{0} ~so~ \pi ~rad = 180^0\]
We always start with pi radians = 180 degrees.
To change from 180 to 135 degrees, divide both sides by 180 and times by 135
thus 135 degrees = pi/180 x 135

In general
\[x^0 = \frac{ x \pi }{ 180 } rad\]

Answer 2

True, \[\pi ~rad=180~\deg\]

Answer 3

From this we could derive the proper conversion factor:\[\frac{ \pi ~rad }{ 180~ \deg}\]

Answer 4

Now multiply 135 deg by this conversion factor. Note how "deg" will cancel out, leaving you with a result expressed in radians, as desired.