Question

I need help! I suck at math, how do you find the sin of 11pi/3 without a calculator??

Answer 1

First remember to get it below \(2\pi\).

Answer 2

\[

11\pi/3 = (6\pi+5\pi)/3 = 2\pi+5\pi/3

\]So the angle is just \(5\pi/3\)

Answer 3

uhh okay i kinda get that! but what about the rest??

Answer 4

Since it's greater than \(\pi\), we can change it to a negative angle: \[
5\pi/3 -2\pi = -\pi/3
\]

Answer 5

how did you just take away the five like that?

Answer 6

\[2\pi = \frac{6\pi}{3}\]

Answer 7

You can add/subtract \(2\pi\) from an angle and the result will be the same because it is the period of the \(\sin\) function.

Answer 8

AND IT ALL MAKES SENSE NOW!!!!

Answer 9

Also remember that \(\sin\) is odd \[
\sin(-\pi/3) = -\sin(\pi/3)
\]

Answer 10

okay, so i have that, but i need like a fraction, and it doesn't seem to be coming out evenly...

Answer 11

how did you know the bottom and side numbers? (sorry if i'm bothering you) i'm trying to figure out my math homework lol

Answer 12

I made a mistake.

Answer 13

and according to my math homework website the correct answer was negative radical 3 over 2...

Answer 14

I see that now haha

Answer 15

Well, start with an equilateral triangle. All sides are length 1, all angles add up to \(\pi\), so they are \(\pi/3\).

Answer 16

Then we cut it in half, to form a right triangle.