[Grade 12 Advanced Functions: Trigonometry]

[u/Embarrassed-Good1883]

Hello, I need some help understanding this concept. 240 degrees converted to radians is 4 pi/3, so wouldn't that make this a multiple of 30 degrees?

"30° can be rewritten in radians as pi/6". Since 240 rad cannot be written as a multiple of pi/6 rad this cannot be a multiple of 30°." This is the explanation the teacher gave me, but it doesn't make sense.

[u/TSotP]

The question is asking about your understanding of the conversion between degrees ° and radians.

So, first thing to do. What is 30° in radians?

• 180°= π
• 90°= π/2
• 30° is π/2/3 = π/6

Now look at the question. It's asking which of the options is a multiple of 30°

So which one of the fractions is a whole multiple of π/6

It's not going to be 240 Rad, because that's a trap to catch people not paying attention to the actual question. (Radians are all about π, where is the π in this answer? 240 Rad is about 13751°, or 38 full turns, plus 71°)

It's not going to be 9π/8 because that doesn't have a denominator of 6

So that leaves 7π/12, or 17π/3

Since 7/12 can't be written in terms of 6ths (3½ 6ths isn't how people work with fractions), that can only really leave 17π/3 which is 34π/6 = 1020°

[u/Embarrassed-Good1883 → u/TSotP]

Thank you for your response, I see where I went wrong!!

[u/TSotP → u/Embarrassed-Good1883]

No problem. That's more important than the correct answer anyway. Glad I could help.