Question

Let (theta) = 2pi/3. Find the exact values of csc(theta), sin(theta), and cot(theta).

Answer 1

\[\LARGE \sin \frac{2\pi}{3}=\sin(120^{0})=\sin(90^0+30^0)=?\]

Answer 2

idk

Answer 3

sin(90+theta)=cos theta
cos30=?

Answer 4

still don't know

Answer 5

Look at this: http://www.mathsisfun.com/geometry/images/circle-unit-304560.gif

Pay close attention to the top right "legend"

It shows that the x-coordinate is cos and the y-coordinate is sin.

Since Θ = (2π/3) or 120°

So \[sin(Θ) = (√3)/2\]
And \[cos(Θ) = (-1/2)\]

Check that with the link i sent you.

This question asks for csc(Θ), sin(Θ), cot(Θ). I'll start with showing you how that works once you give me the all-clear that you see where i'm going so far.

Answer 6

all clear!

Answer 7

I'll start with csc(Θ)

csc(Θ) = 1/cos(Θ)

From the previous work I mentioned that the cos(120) = -(1.2)

So:

\[\csc (120) = \frac{ 1 }{ \cos (120)} \]
\[\csc (120) = \frac{ 1 }{ -\frac{1}{2}} \]