Trig general solutions quick question (1 Viewer)

[malcolm21]

http://puu.sh/ipBwf/6410588337.png

got all the way to the very end, got the first solution, 2n(pi) + tan^-1(2/3), subbed in pi and found that it was a solution, but I don't know how to put that pi into the general solution form?

 

[InteGrand]

http://puu.sh/ipBwf/6410588337.png

got all the way to the very end, got the first solution, 2n(pi) + tan^-1(2/3), subbed in pi and found that it was a solution, but I don't know how to put that pi into the general solution form?

 

[malcolm21]

where'd you get the two from?

I don't know how to put the pi into the general solution

kpi + tan^-1(??)

 

[InteGrand]

where'd you get the two from?

I don't know how to put the pi into the general solution

kpi + tan^-1(??)

Because of the periodicity of the original LHS function (it has period , as can be seen using auxiliary angle method, or inferred intuitively seeing that if we increase the argument by an integer multiple , the function value is the same).

(This periodicity of the trig. functions is the reason for the use of "" (or in the case of tan, , since tan's period is just rather than like sine and cosine) in the general solutions.)