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Homework Statement
Solve for 0 ≤ θ ≤ 2π (pi). Give the exact values.
tan^2θ=2tanθsinθ
I'm not sure how to go about this one =/
Dunkle said:The [tex]cos(\theta) = 1/2[/tex] is correct, but I don't know how you arrived at [tex]cos(\theta) = 0[/tex]. If [tex]cos(\theta) = 0[/tex], then [tex]tan(\theta)[/tex] is undefined. Although both sides are undefined, it does not mean they are equal. That would be similar to saying 1/0 = 0/0, which is not true! Also, remember there are two solutions for [tex]cos(\theta) = 1/2[/tex] on [tex][0,2\pi][/tex], one of them is [tex]\pi/3[/tex] as you mentioned. What do you think the other one is? Drawing a graph out might help.
rought said:I'm not sure how to go about this one =/
rought said:the other one would be 5π/3
here's what I did
tan^2θ=2tanθsinθ
sin^2 θ/cos^2 θ=2(sinθ/cosθ).sinθ
sin^2 θ/cos^2 θ=2(sin^2 θ/cosθ)
1/cos^2 θ=2/cosθ
2cos^2 θ-cosθ=0
cosθ(2cosθ -1)=0
cosθ=0 and 2cosθ -1=0