Proving a Cofunction Identity
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Proving a Cofunction Identity

[From: ] [author: ] [Date: 11-06-07] [Hit: ]
you can subtract 2π from 3π and then evaluate since were dealing with a unit circle (0 and 2π are the same thing on a unit circle,Since sin(π) = 0 and cos(π) = -1,......
I don't get this at all, so start from the beginning. First best answer gets 10 points!

55. sin(3pi - x) = sinx

How come it's sin3pi cosx, not sin3pi sinx?

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You can use the subtraction formula for sin: sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

For sin(3π - x), a is 3π and b is x:
sin(3π)cos(x) - cos(3π)sin(x))

To evaluate sin and cos of 3π, you can subtract 2π from 3π and then evaluate since we're dealing with a unit circle (0 and 2π are the same thing on a unit circle, therefore π is the same as 3π)

sin(π)cos(x) - cos(π)sin(x)
Since sin(π) = 0 and cos(π) = -1, we are left with:
-(-sin(x))
= sin(x)
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keywords: Identity,Cofunction,Proving,Proving a Cofunction Identity
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