inverse trig help (1 Viewer)

[darkphoenix]

differentiate cos^-1(sinx)

I got -cos/ square root (cos^2(x)) so cos cancel out and is -1.
But the answer is +- 1. I don't really understand it... can any one explain? Thanks

 

[RishBonjour]

wolfram alpha gets negative 1 too (as expected). are you sure the answer isn't wrong?

 

[darkphoenix]

well its from excel 3 u , it says that +-1, as cosx -+, i am not sure whether is it to do with the absolute value thing or not. Not sure whether the answer is correct or not...

 

[Carrotsticks]

The answer is plus/minus 1, and you can observe that if you sketch the graph (looks like a zig-zag).

The curve cos(x) is positive and negative, depending on which X value you take.

So when you take the root of cos^2(x), you must break it up into 'cases'. One for when cos(x) is positive and another for when it is negative.

It's not the same thing as taking the root of a NUMBER because a number in itself (as far as you know) is either positive or negative, can't be both at the same time.

However, we are dealing with a FUNCTION, which in this case CAN be both positive AND negative. So we must take cases.

 

[darkphoenix]

The answer is plus/minus 1, and you can observe that if you sketch the graph (looks like a zig-zag).

The curve cos(x) is positive and negative, depending on which X value you take.

So when you take the root of cos^2(x), you must break it up into 'cases'. One for when cos(x) is positive and another for when it is negative.

It's not the same thing as taking the root of a NUMBER because a number in itself (as far as you know) is either positive or negative, can't be both at the same time.

However, we are dealing with a FUNCTION, which in this case CAN be both positive AND negative. So we must take cases.

Thank you, I sort of get it, so that means if cosx is a negative, the root of cos^2(x) is still a positive cosx but the numerator is a negative cosx so when times with -1 = +1 right? Can you show me how to write the answer in exam form

 

[Sy123]

Well if you sketch the derivative, you get the zig zag. However the zig zag is a result of the division of two seperate functions. That is, if we skecth the top and bottom functions on the same plane, we get.

Where the blue is y=cos(x) and the red is the denominator with the square root function, the red is the function NOT simplified and this makes a huge difference and is necessary in explanation.
The purple is where the curves are the same. So when we divide these two, no matter what values, we will get 1 for all the purple values. For the red and blue ones however, if you notice, they are symetrical, they are basically the same curve flipped, so when you divide these no matter what value you get it will be -1.

 

[darkphoenix]

Right, thank you all, i got it