The Student Room Group

Where does the minus come from?

So I'm following a worked example in a book, for C3, and I've learned that sin(x + pi) = -sin(x). Where does the minus come from?
Does looking at a graph help?

Original post by HandmadeTurnip
Does looking at a graph help?


No, it doesn't, sorry.
Original post by melvisntnormal
No, it doesn't, sorry.


Look at the values of y in the range 0<x<pi and then look at its values in the range pi<x<2pi, can you see that they're exactly the same values except the latter are negative?
Original post by HandmadeTurnip
Look at the values of y in the range 0<x<pi and then look at its values in the range pi<x<2pi, can you see that they're exactly the same values except the latter are negative?

Yeah I can see that...
Original post by melvisntnormal
Yeah I can see that...


So if you take any of the x values from that first range and add pi to it, the resulting y value will be the same as it was originally, just negative. It's all to do with the periodicity of the function.
Reply 6
Try the addition formula, sin(A+B) = ...
Original post by HandmadeTurnip
So if you take any of the x values from that first range and add pi to it, the resulting y value will be the same as it was originally, just negative. It's all to do with the periodicity of the function.

OK, i think I understand that...
Reply 8
Original post by melvisntnormal
OK, i think I understand that...


Note that the graph isn't the reason for the relationship - the graph is a consequence of the relationship!

If you want to understand WHY it's true, think about the definition of cos and sin as the x and y coordinates of a point moving round the unit circle. What happens to the y coordinate (sin) if you start with a point in the first quadrant and add pi radians to its angle (i.e. the angle the radius vector makes with the positive x axis)?

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