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Question: How to solve it with Maple?

Question:How to solve it with Maple?

Markiyan Hirnyk 7809 Maple
solve trigonometry
November 26 2012
0

 

How to solve it with Maple? The explicit and nonnumerical solution is required. 
restart; Digits := 20; solve(cos(x^2+x)+cos(x+2*Pi*(1/3))+cos(x+4*Pi*(1/3)) = 0, allsolutions)

RootOf(-cos(_Z^2+_Z)+sin(_Z+(1/6)*Pi)+cos(_Z+(1/3)*Pi))

 (1)

sol1 := fsolve(cos(x^2+x)+cos(x+2*Pi*(1/3))+cos(x+4*Pi*(1/3)) = 0)

0.

 (2)

sol2 := fsolve(cos(x^2+x)+cos(x+2*Pi*(1/3))+cos(x+4*Pi*(1/3)) = 0, x, avoid = {x = sol1})

-2.0000000000000000000

 (3)

sol3 := fsolve(cos(x^2+x)+cos(x+2*Pi*(1/3))+cos(x+4*Pi*(1/3)) = 0, x, avoid = {x = sol1, x = sol2})

2.6832554370229568635

 (4)

identify(sol3)

2.6832554370229568635

 (5)

plot(cos(x^2+x)+cos(x+2*Pi*(1/3))+cos(x+4*Pi*(1/3)), x = -10 .. 10)

  

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