Tutoring math, you deal with degree-to-radian conversions.  The math tutor continues on the topic of radians, picking up where he left off last July.

 
To know what a radian is, see my post here. In math 12, radians – “rads” – are introduced. In calculus, they are used almost exclusively.

As I earlier observed,

2π rads=360°

Commonly, “rads” isn’t written; the unit is just understood.

From 2π=360° it follows that

π=180°

Dividing both sides by 3, we get

π/3=60°

Dividing both sides by 6, we arrive at

π/6=180°/6=30°

Returning to the equation π=180° let’s divide both sides by 4 this time. We arrive at

π/4=180°/4=45°

For exact values, we have all we need for most conversions.

Example 1: Convert 210° to rads.

Solution: Realize that 210 = 7(30). Knowing that 30°=π/6, it follows that

210°=7π/6

Example 2: Now, let’s go the other way: give 3π/4 in degrees.

Solution: We recall that π/4=45°. Then it follows that

3π/4=3*45°=135°

The fraction-to-multiple method above is very quick once you remember the simple radian fractions and what they are in degrees. For most exact value conversions, it’s what you need:)

In a future post I’ll be exploring the conversion between radians and degrees when it’s not an exact value.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.