Math: Radians, Part II
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.
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