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know anything about trig?

(16 Posts)
albedo Tue 24-Oct-17 17:13:35

This might be a stupid question, but...

The integral of sinx is -cosx

Integration is the area under a line/curve

The area under a sine wave between 0 and pi is 2.

You see where I'm going with this. There ain't no 2 on a -cosx curve.

I'm sure my thinking is wrong somewhere. But where? grin

JustRichmal Tue 24-Oct-17 22:09:06

I hope someone comes along soon with the right answer, but if you add 1 as the constant of integration, does that work?

Where is Noblegiraffe when you need her?

tissuesosoft Tue 24-Oct-17 22:16:32

Is it - cos pi/2 (- cos 0) so - 0 - (-1)

tissuesosoft Tue 24-Oct-17 22:22:57

Ignore me, think I just answered a question that I didn't read properly confused

albedo Tue 24-Oct-17 22:28:03

Do you add a constant of integration for a definite integral?

Good lord I wish I'd paid more attention in maths blush

DadDadDad Tue 24-Oct-17 22:32:58

Area under sine curve between 0 and pi is (-cos (pi)) - (-cos(0)), ie you evaluate the function -cos(x) at both ends of the interval. As cos(pi) = -1 and cos(0) = 1 this area evaluates to:

-(-1) - (-1) = 1 + 1 = 2.

tissuesosoft Tue 24-Oct-17 22:36:33

The constant is not completely necessary, because it will be taken away (minus) when the integral is evaluated. But it is a good idea to keep the constant of integration.

DadDadDad Tue 24-Oct-17 22:42:57

Second curve shows the area from zero to x under the sine curve as a function of x. It is an upside-down cos curve shifted up 1, so it does indeed go to 2.

JustRichmal Tue 24-Oct-17 22:47:57

So if you integrate sine x curve which is zero when x=0, will it be -cos x +1?

DadDadDad Tue 24-Oct-17 22:53:08

If you integrate as an indefinite integral it will be -cos(x) + C.

If you want the area (definite integral) between zero and x then it will be -cos(x) - -cos(0) = -cos(x) + 1.

If you said, "the area function must take the form -cos(x) + C, and I want to measure the area from zero", then the area function must start at zero when x=0, and that leads to the same conclusion, ie that C = 1, and the area function is -cos(x) + 1.

If you wanted to measure the area between say pi/2 and x, then the answer would be different.

albedo Tue 24-Oct-17 22:55:54

So it goes from zero to two instead of -1 to 1 and they decided just to shift it down a bit?

albedo Tue 24-Oct-17 22:57:14

Ohhhhhhh yes i see what was being said about the constant of integration.

Makes sense, thank you!

DadDadDad Tue 24-Oct-17 23:06:30

OK, now come over to this thread, and join the debate about maths in schools! smile

JustRichmal Tue 24-Oct-17 23:18:15

albedo thanks for posting this question. Something I never thought to think about has helped trig make more sense to me.

albedo Tue 24-Oct-17 23:21:16

DadDadDad grin

In all seriousness though, my grasp of basic maths is atrocious and I liked my maths lessons at school! I totally understand why people back slowly away from it with their hands over their eyes.

albedo Tue 24-Oct-17 23:23:22

@justrichmal I'm super into trig atm because of my line of work - if you've not already seen it, check out how a rotating vector makes a sine wave and how the triangles and angles come into it. So cool!

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