Question 657867: cos^-1(cos(5))
The answer in the book is 2pi-5 but my answer is just 5. Can you please explain it? Thanks.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! cos^-1(cos(5))
The answer in the book is 2pi-5 but my answer is just 5. Can you please explain it? Thanks.
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I will give it a try:
The angle of 5 radians is in quadrant IV where cos>0, but the domain of a cosine inverse function by definition is [0,π], so 2π-5 is like moving the reference angle to quadrant I, that part of the domain where cos>0.
note: The reference angle of 5=-(2π-5)=-1.28 (in quadrant IV)
The reference angle of (2π-5)=2π-5=1.28 (in quadrant I)
Identity: cos(x)=cos(-x)
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