How solve this trigo system ?

[Dieter]

(09-18-2017 08:56 AM)ggauny@live.fr Wrote:  I would like solve my exercize with my Prime but I dont' know
how to do.

The system is :

cos x - cos y = 1/2
sin x * sin y = 3/8

I have tryied all things with SOLVE but no good it is.

It you want to use a solver there is another, shorter solution.

This is a nonlinear equation system with two unknowns. One way to solve such a system is the substitution method which has already been discussed. Another approach is solving both equations for the same variable, i.e. for x or y, and set equation1 = equation2:

y = arccos(cos x – 0,5)
y = arcsin(0,375 / sin x)

=>  arccos(cos x – 0,5) = arcsin(0,375 / sin x)

Now any decent solver should be able to solve this (x=24,2952° => y=65,7048°).
Which does not mean that any solver will return all possible solutions. ;-)

AFAIK on the Prime you can also find the intersection of both graphs, which should return the same result.

Dieter