Basic integral question & sin, tan, cos.

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October 19th 2012, 01:02 PM
uperkurk

Basic integral question & sin, tan, cos.

I've just been looking at some algebra called intergrals.

$f(x) = 3x^4+x^2-9x+1 = F(x)\frac{3x^5}{5}+\frac{x^3}{3}-\frac{9x^2}{2}+x+c$

I understand this fully but in the next step when he simplifies it a little he turns the $\frac{x^3}{3}$ into $\frac{1}{3}x^3$

I don't understand why he put a 1 there in place of the $x^3$ . Where did the 1 come from? Also one other question I have which I have is:

$f(x)= \sin x = F(x)= -\cos x+c$

I have a basic understand of sin, cos and tan but what exactly do the represent when used in equations?

Can someone just explain what these equation actually means? Thanks
October 19th 2012, 01:13 PM
MarkFL

Re: Basic integral question & sin, tan, cos.

$\frac{x^3}{3}=\frac{1\cdot x^3}{3\cdot1}=\frac{1}{3}\cdot\frac{x^3}{1}=\frac{ 1}{3}x^3$

If you look at the graph of $y=-\cos(x)+C$ (choose any $C$ ) and then simultaneously plot the graph of $y=\sin(x)$ you will see that the second graph represents the instantaneous rate of change of the first.
October 19th 2012, 01:23 PM
uperkurk

Re: Basic integral question & sin, tan, cos.

But that's just it, what is -cos, cos, tan, sin etc? Are they actual constants like PI=3.14 etc? Would you be able to plot a graph $y=\-cos(x)+4$ just so I can see what value -cos represents.
October 19th 2012, 01:28 PM
uperkurk

Re: Basic integral question & sin, tan, cos.

I've just been looking at a cheat chart and I think something like $y = -cos(60)+4$ the $-cos(60)$ would represent $-\frac{1}{2}$ ?
October 19th 2012, 01:30 PM
MarkFL

Re: Basic integral question & sin, tan, cos.

I'm sorry, you stated you have a basic understanding of the trigonometric functions, so I naturally assumed that you did.

There are many sites online that will graph functions, and to essentially teach trigonometry is beyond the scope for me in online posts. There is a great deal of online material though that can get you started. Just do a search on trigonometry.

I highly recommend you learn this before exploring the calculus!
October 19th 2012, 01:37 PM
uperkurk

Re: Basic integral question & sin, tan, cos.

Oh ok no problem, I thought this was still algebra, I must have been getting a bit carried away :D
October 19th 2012, 02:50 PM
gp8283

Re: Basic integral question & sin, tan, cos.

I would recommend checking out Khan Academy there are videos that you can watch for trigonometry and also practice problems for this topic.