Question 735822: when finding the values of inverse trigonometric functions, how do you get from.. Cos-1 (-0.5) =x cos x = -0.5 and 0_< x _< pi to Cos -1 (-0.5) = 2 pi over 3?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! when finding the values of inverse trigonometric functions, how do you get from.. Cos-1 (-0.5) =x cos x = -0.5 and 0_< x _< pi to Cos -1 (-0.5) = 2 pi over 3?
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Cos -1 (-0.5) = 2 pi over 3
Inverse cos(-0.5)=2π/3
This reads: (2π/3 is an angle between 0 and π whose cos is= (-0.5)
This also means the angle must be in quadrant I or quadrant II.
cos>0 in quadrant I and cos<0 in quadrant II
So the angle must be in quadrant II since the given cos inverse =(-0.5)<0.
If given cos inverse was (0.5)>0, the angle would be in quadrant I=π/3 instead of 2π/3 in quadrant II
By definition, the cos inverse domain is restricted to [0,π]
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