Question

PLSS HELP!!! MEDALS!!!




Find the exact value of cos(4pi/3):
I know no that it is -1/2, but my original answer was -sqrt3/2, so I guess I just solved for the wrong angle. Can someone help me with this so I don't make this mistake again? Thanks!

Answer 1

First, do you know how to convert radians to degrees?

Answer 2

4*180/3 = 240 degrees
cos(240)

Answer 3

Then you have to reference that to the x-axis, which the closest being 180 degrees.
Therefore,
240-180 = 60
cos(60)

Answer 4

Then, hopefully, you have what I call it in school, the "chart of death" memorized, where cos(60) = -1/2

Answer 5

Well, cos(60) = .5, but you have to remember, since it is in the third quadrant, it will be negative.

Answer 6

For problems like these, I would say you ask yourself these quesetions: What's the reference angle for \(\frac{4\pi}{3}\)? What is the x-value on the Unit Circle of that reference angle?
(Hint: the reference angle is \(\frac{\pi}{3}\))

Answer 7

Oh okay right I forgot about the reference angle thingamajig. I was finding the angle from the terminal arm to the y axis but I should have been finding the angle from the terminal arm to the x axis. Thanks so much @kittiwitti1 !

Answer 8

No problem ! :)

I use the Left-Hand Rule (LHR) to remember the sin and cos values for the reference angles, which are \(\frac{\pi}{6},\frac{\pi}{4}\text{ and }\frac{\pi}{3}\), or 30, 45 and 60 degrees, respectively.

Answer 9

LHR here: http://www.foresthills.edu/userfiles/161/Classes/5071/The%20Finger%20Trick%20for%20Trig.pdf