Sketching Angles and Radians

Converting between Angles and Radians

Goal: To convert angles from degrees to radians and vice versa.

Radians

A radian is the standard unit of angular measure. This is because they are easiest to work with mathematically. Because the radian is related to the radius of a circle, radian measures can be used in trigonometric calculations easier than degrees.

Radians

Recall that the arc length of a complete rotation is the circumference, where the formula is equal to 2π times the length of the radius. So, in terms of radian measure, a complete rotation (360 degrees) is 2π radians.

Since 2π radians = 360°, we can create a conversion factor.

Radians

Convert 125° to radians.

Fill in the Blank

Convert $$\frac{3\pi}{8}$$  radians to degrees.

Multiple Choice

Convert 150° to radians.

• $$\frac{5\pi}{6}radians$$ radians

• $$30\pi$$ radians

• $$330\pi$$ radians

• $$\frac{5\pi}{6}$$ radians

Open Ended

After going through this lesson, which type of problem(s) do you feel like you can do well? Explain.

Open Ended

After going through this lesson, which type of problem(s) do you feel like you are still struggling with? Explain.