When finding the exact value of a trig function...

[abel muroi]

how do i know if the value is negative or positive?



lets say for example i was given the problem cos (-7/3 pi) and was told to find the exact value of the function..

since cos (-7/3 pi) is -2 1/3 that means that the angle is below the x axis so i am assuming the value is negative right?




so the answer has got to be -1/2 right?

 

[Steven G]

how do i know if the value is negative or positive?



lets say for example i was given the problem cos (-7/3 pi) and was told to find the exact value of the function..

since cos (-7/3 pi) is -2 1/3 that means that the angle is below the x axis so i am assuming the value is negative right?




so the answer has got to be -1/2 right?

If cos (-7/3 pi) is -2 1/3 then how can you think that the answer (to cos (-7/3 pi)) is -1/2? The answer (according to you) is -2 1/3! My next question is how can cosine of any angle be less than -1? If the the terminal point of theta is to the left of the y-axis then cos(theta) is negative.

 

[ksdhart]

Your method seems mostly fine to me, but what seems to have you confused is positive vs negative angles. A negative angle will affect the answer for sine, but not cosine. Because cosine is an even function (and mirrored about the y-axis), $\displaystyle cos(x)=cos(-x)$. So, $\displaystyle cos\left(\frac{-7\pi }{3}\right)=cos\left(\frac{7\pi }{3}\right)$. Try solving from there. If you need more help, just let us know.

 

[Steven G]

Your method seems mostly fine to me, but what seems to have you confused is positive vs negative angles. A negative angle will affect the answer for sine, but not cosine. Because cosine is an even function (and mirrored about the y-axis), $\displaystyle cos(x)=cos(-x)$. So, $\displaystyle cos\left(\frac{-7\pi }{3}\right)=cos\left(\frac{7\pi }{3}\right)$. Try solving from there. If you need more help, just let us know.

What you wrote is all true, but it is also true that if the angle is to the left of the y-axis then the cosine of this angle is negative.

 

[pka]

What you wrote is all true, but it is also true that if the angle is to the left of the y-axis then the cosine of this angle is negative.

Is that actually what we have here? Look at this.