Finding the general solution for trigonometric equation Solve for general solutions tan(x/3)=1

Vincent Norman

Vincent Norman

Answered question

2022-10-30

Finding the general solution for trigonometric equation
Solve for general solutions
tan ( x / 3 ) = 1
When I solve this equation my answer comes to be x = 3 π / 4 ± 2 n π , 15 π / 4 ± 2 n π where n is an integer
However when I graph the equation y = tan ( x / 3 ) 1 values for x such as 11 π / 4 do not equal zero.
What would x be equal to then?

Answer & Explanation

silenthunter440

silenthunter440

Beginner2022-10-31Added 19 answers

The general solution can be described as
x 3 π 4 ( mod π ) x 3 π 4 ( mod 3 π )
since the tangent function has period π
cousinhaui

cousinhaui

Beginner2022-11-01Added 5 answers

Hint:
General solution of tan x is
tan x = a x = arctan a + k π , k Z
where is period is π not 2 π

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