0 like 0 dislike
Solve the the equation tan(x+pi/3) = sqrt 3/3 over the interval [0, 2].

1 Answer

0 like 0 dislike
Rewrite the right side as √3/3 = 1/√3, and recall that tan(x) = 1/√3 when x = π/6. Then since tan is π-periodic, taking the inverse tan of both sides gives

[tex]\tan\left(x + \dfrac\pi3\right) = \dfrac1{\sqrt3} \implies \tan^{-1}\left(\tan\left(x + \dfrac\pi3\right)\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) + n\pi[/tex]

[tex]\implies x + \dfrac\pi3 = \dfrac\pi6 + n\pi[/tex]

where n is any integer. Solving for x, we get

[tex]x = -\dfrac\pi6 + n\pi[/tex]

and the solutions in the interval [0, 2π] are x = 5π/6 and x = 11π/6 (for n = 1 and n = 2).
Welcome to AskTheTask.com, where understudies, educators and math devotees can ask and respond to any number related inquiry. Find support and replies to any numerical statement including variable based math, geometry, calculation, analytics, geometry, divisions, settling articulation, improving on articulations from there, the sky is the limit. Find solutions to numerical problems. Help is consistently 100 percent free!


No related questions found