Manipulating a trigonometric equation involving tan 2 ⁡ ( 3 θ )If tan 2 ⁡ 3 θ = 1, how do I manipulate the equation so I can make tan ⁡ θ the subject? I forgot how to do these since it has been a long time. I tried searching before posting. My answer is 1 3 , not sure if it is correct though.

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Manipulating a trigonometric equation involving       tan    2    ⁡  (  3  θ  )If       tan    2    ⁡  3  θ  =  1, how do I manipulate the equation so I can make   tan  ⁡  θ the subject? I forgot how to do these since it has been a long time. I tried searching before posting. My answer is       1          3      , not sure if it is correct though.

Ramiro Sosa · Accepted Answer

tan    2    ⁡  (  3  θ  )  =  1    ⟺              tan      2        ⁡    (    3    θ    )    =  ±      1      ⟺    tan  ⁡  (  3  θ  )  =  ±  1Then                    (I)                    θ        =                  1          3                          tan                      −            1                          ⁡        (        1        )            or                    (II)                    θ        =                  1          3                          tan                      −            1                          ⁡        (        −        1        )              (  I  )  θ  =      1    3    (      45          ∘        )  =      15    ∘    or  θ  =      1    3    (      225    ∘    )  =  75  ∘ or  θ  =      1    3    (      405    ∘    )  =      135    ∘   or   θ  =      1    3    (      585    ∘    )  =      195    ∘   or  θ  =      1    3    (      765    ∘    )  =      255    ∘   or  θ  =      1    3    (      945    ∘    )  =      315    ∘  I assume you are looking for solutions in   0  ≤  θ  ≤      360    ∘  Can you do the same for   (  I  I  )?

Manipulating a trigonometric equation involving tan^2(3 theta)

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