Question

what is cos 2pi/3?
a. -3sqrt/2
b. sqrt 3/2
c. -1/2
d. 1/2 ( i think its b or c)

Answer 1

Convert it into degrees if that helps; or draw a unit circle if that helps

Answer 2

120'

Answer 3

What's its supplementary angle?

Answer 4

Formula: \(\cos(180^\circ-\theta)=-\cos\theta\)

Answer 5

60?

Answer 6

Or you can use \(\cos(90^\circ+\theta)=-\sin\theta\) which is more standard

Answer 7

Choose one of the formulas that I gave you

Answer 8

the first one.

Answer 9

Then use it

Answer 10

but what do i use in place of the theta?

Answer 11

60`

Answer 12

in both of them?

Answer 13

Both of what? You've chosen a formula already

Answer 14

yes. but do i put 60 in both of the thetas?

Answer 15

\[\cos120^\circ=\cos(180^\circ-60^\circ)=\cdots\]

Answer 16

P.S. Schools prefer the second formula

Answer 17

So I'll use the first formula and you'll try to use the second formula.
Using the first formula: \(\cos120^\circ=\cos(180^\circ-60^\circ)=-\cos60^\circ=-0.5\)

Answer 18

-1/2?

Answer 19

Yes

Answer 20

Standard method: \(\displaystyle\cos\frac{2\pi}3=\cos\left(\frac\pi2+\frac\pi6\right)=-\sin\left(\frac\pi6\right)=-\frac12\)