# Thread: trigonometry

1. ## trigonometry

hi!
Can someone teach me how to solce arccos(cos(7Pi/ 6))?

i tried to change 7pi/ 6 into the principal angle but what i thought of was:

cos (7pi/6)= -cos (pi/6)

although it is in the principal angle, i do not know how to continue after that.

thanks!

2. Originally Posted by alexandrabel90
hi!
Can someone teach me how to solce arccos(cos(7Pi/ 6))?

i tried to change 7pi/ 6 into the principal angle but what i thought of was:

cos (7pi/6)= -cos (pi/6)

although it is in the principal angle, i do not know how to continue after that.

thanks!
HI

it would be $\frac{5\pi}{6}$

cos (7pi/6)= -cos (pi/6)=cos (5pi/6)

Lets say

$\cos^{-1} \cos (\frac{5\pi}{6})=x$

$\cos (\frac{5\pi}{6})=\cos x$

So now , cancel the 'cos' , thus $x=\frac{5\pi}{6}$

Note that its different when its $\cos \cos^{-1}$ something

3. but i thought that way that you did only applies to when the angle is in the principal range of 0 to 180 degrees?

so i was trying to convert 7pi/6 into the principal angle of cos x where x is in the principal range so that i can use the method that you have just used..

4. Originally Posted by alexandrabel90
but i thought that way that you did only applies to when the angle is in the principal range of 0 to 180 degrees?

so i was trying to convert 7pi/6 into the principal angle of cos x where x is in the principal range so that i can use the method that you have just used..
yeah you are right , i just edited .

### In cos-1(cos7pi/6) why it is not cos-1(cospi pi/6)

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