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?
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)
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)