Question 526607: How would you go about solving arccos(sin(6)) where 6 is in radians and you cannot use a calculator? The exact value answer is 5pi/2 - 6.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How would you go about solving arccos(sin(6)) where 6 is in radians and you cannot use a calculator? The exact value answer is 5pi/2 - 6.
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There is an identity: cos(90º-x)=sinx
In radian form, cos(π/2-x)=sinx
so, arccos(sin(6)=arccos(cos(π/2-6))
The inverse of its function is the angle of the function, (π/2-6) radians
The answer you gave, 5π/2-6 will give you the same value, cos(π/2-6)=-0.279415, cos(5π/2-6)=-0.279415.
In fact, I found that any odd multiple of π/2, like 3π/2, 7π/2, 9π/2, etc will give the same value of the cos of the angle. So, the answer should be nπ/2-6, n=odd integer
I am not yet smart enough to figure out why this is so. Maybe your teacher can explain.
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