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Question Number 194327 by pete last updated on 03/Jul/23
If ta4θ = 1, find the values of θ.
$$\mathrm{If}\:\mathrm{ta4}\theta\:=\:\mathrm{1},\:\mathrm{find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\theta. \\ $$
Answered by MikeH last updated on 03/Jul/23
tan 4θ = 1   ⇒ 4θ = πn + (1/4)π  ⇒ θ = (1/4)πn + (1/(16))π  θ = {(1/(16))π, (5/(16))π, (9/(16))π,...}
$$\mathrm{tan}\:\mathrm{4}\theta\:=\:\mathrm{1}\: \\ $$$$\Rightarrow\:\mathrm{4}\theta\:=\:\pi{n}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\pi \\ $$$$\Rightarrow\:\theta\:=\:\frac{\mathrm{1}}{\mathrm{4}}\pi{n}\:+\:\frac{\mathrm{1}}{\mathrm{16}}\pi \\ $$$$\theta\:=\:\left\{\frac{\mathrm{1}}{\mathrm{16}}\pi,\:\frac{\mathrm{5}}{\mathrm{16}}\pi,\:\frac{\mathrm{9}}{\mathrm{16}}\pi,…\right\} \\ $$
Commented by pete last updated on 04/Jul/23
thank you sir
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

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