New Help, Cannot Seem to Get it

  • Thread starter Thread starter alexparker
  • Start date Start date
alexparker
Messages
18
Reaction score
0
Prove that (d/dx)arcos(x) = -1/(Sqrt(1-x^2)


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
cos is the inverse function of arccos. So cos(arccos(x))=x. Differentiate both sides. Did you try that?
 
Or: if y= arccos(x) then x= cos(y). Differentiate that to find dx/dy= -sin(y) so that
dy/dx= -1/sin(y)= -1/sin(arccos(y)).

Use trig identities to simplify that (change sin(arccos(y)) to cos(arccos(y))=y) or think about a right triangle with "near side" of length y and hypotenuse of length 1. What is the length of the "opposite side"? Whatr is the sine?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Prove that the integral is equal to ##\pi^2/8##
2
Replies
96
Views
4K
Solve the given second order differential equation
Replies
14
Views
1K
How Does Substitution Affect Double Integration and Differentiation?
Replies
3
Views
1K
How should I use the Jacobi equation to show this?
Replies
4
Views
2K
How should I show that the transformation makes the system Hamiltonian?
Replies
4
Views
2K
Volume between a region (above x-axis and below parabola) and a surface
Replies
4
Views
2K
Calculating radius of gyration of plane figure about x-axis
Replies
5
Views
2K
Verify Green's Theorem in the given problem
Replies
10
Views
2K
How to Integrate [1/(x^2 + 3)] dx?
Replies
5
Views
3K
Can anyone please verify/confirm these derivatives?
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top