Items tagged with trigonometry trigonometry Tagged Items Feed

Greetingsi

Maple does not simplify the expression -2*Pi*sin(Pi*a)/(-1+cos(2*Pi*a)). How can I make it do so? 

Thanks,

Maple 15 64-bit on Windows 7

HI all,

I am trying to figure out in MAPLE how can I write     A * sin*theta + B* cos* theta  in the form as follows:

                                                   ...

How to make Maple recognize that: sin(x) +sin(x+Pi/3) is equivalent to sqrt(3)sin(x+Pi/6), and various variants of this expression involving sine, cosine, constants equal to Pi/3, Pi/6, etc? I can do it using the subs finction, but this involves finding the equivalent by hand for each variant. Thanks.

For the following system:

x1 := M*(cos(phi)-a*cos(3*phi)) / (1-b*cos(2*phi))

x2 := M*(cos(phi)+a*cos(3*phi)) / (1+b*cos(2*phi))

y1 := M*(sin(phi)-a*sin(3*phi)) / (1-b*cos(2*phi))

y2 := M*(sin(phi)+a*sin(3*phi))/ (1+b*cos(2*phi))

I'd like to find M(x1,x2,y1,y2) if possible; that is, I'd like to solve for M in terms of x1, x2, y1, and y2, eliminating a, b, and phi.

I've tried

solve({x1=X1, x2=X2, y1=Y1, y2=Y2},{M,a,b,phi},AllSolutions);

Update - April 4, 2011: I corrected a typo in Table 2, first column, bottom row.  What was sqrt(6) has been changed to sqrt(5).