# solving system of equations produce complex numbers 2

mrahikka shared this problem 2 years ago
Not a Problem

2nd try

Why does this system of equations give complex roots for solution?

1

maybe because of the entry mode (use of cos and sin)

try u = cos(a), v = sin(a)

and linearise cos(2a) and sin(2a) before using ratkaise

but it's better to solve with just a pen because this is just two lines

1

This seems OK:

`Solve({(-3sin(a) + y = (-3a + x) cos(a)),TrigExpand((-cos(2a) + y = -2 (-a + x) sin(2a)))},{x,y})`

1

Also simplifying the answer is fine:

`Simplify(Solve({(-3sin(a) + y = (-3a + x) cos(a)),(-cos(2a) + y = -2 (-a + x) sin(2a))},{x,y}))`

Sorry, there's no other improvement we can make with this

1

I can undertand that this can very easily be solved without a computer. My question was why. Does this mean that if I have equations with constansts cos(2a), sin(2a) and a, there is a possibility that I get complex roots?

Thanks Mike telling about the Simplify and trigexpand

M

1

`Does this mean that if I have equations with constansts cos(2a), sin(2a) and a, there is a possibility that I get complex roots?`

Sorry, yes