Solving for Exact Value: cos(2pi/3) = x

[theschaef]

cos(2pi/3) = x

This is on an old calculus exam. It tells me that the answer is -1/2 but I'm not quite sure how they solved that. How can I come to this answer?

 

[stapel]

Use what you learned back in trig. What are your basic reference angles? What are the basic reference-angle values? What does the cosine wave look like?

Eliz.

 

[pka]

I think that one should know the more widely used ‘angles’.
2pi/3 is just one of them its reference angle is pi/3.
You should learn all of pi/6, pi/3, pi/4, pi/2 etc.

 

[maverick812254]

What kind of answers are those? All you did was ask questions....Is there actually some special triangle or something that could be used to solve that?

 

[pka]

What kind of answers are those? All you did was ask questions....Is there actually some special triangle or something that could be used to solve that?

Whom are you addressing there?
Both answers are perfectly reasonable.
The point is there is really no way to solve it except to understand the values of the so-called ‘special angles’: those that I listed. One learns them. Then if one understands reference angles, working such problems is simple.

 

[stapel]

Is there actually some special triangle or something that could be used to solve that?

The questions I asked were a leading series, the answers to which would have led you quickly to the solution. But they appear to be utterly unfamiliar material to you...?

Have you not taken trigonometry yet?

Eliz.

 

[skeeter]

What kind of answers are those? All you did was ask questions....Is there actually some special triangle or something that could be used to solve that?

yes ... a 30-60-90 right triangle is the reference triangle for 2pi/3 radians in quadrant II.

are you familiar with the side relationships of such a triangle?