3tan (x- pi/5)-sqrt(3) =0
3tan (x- pi/5)-sqrt(3) =0, I will assume you want 0 ≤ x ≤ 2π
3tan (x- pi/5) = √3
tan (x- pi/5) = √3/3
angle in standard position: tan Ø = √3/3, Ø = appr .5236 radi
but the tangent is also positive in III so Ø = π + .5236
case 1:
x - π/5 = .5236
x = 1.1519
case 2:
x - π/5 = π + .5236
x = 4.2935
tan (x- π/5) = √3/3
so, x - π/5 = π/6 or 7π/6
x = 11π/30 or 41π/30
To solve the equation 3tan(x - π/5) - √3 = 0, we can follow these steps:
Step 1: Start by isolating the tangent term.
Add √3 to both sides of the equation:
3tan(x - π/5) = √3
Step 2: Divide both sides of the equation by 3 to isolate the tangent term.
tan(x - π/5) = √3 / 3
Step 3: Take the inverse tangent (arctan) of both sides to determine the angle value.
x - π/5 = arctan(√3 / 3)
Step 4: Add π/5 to both sides of the equation.
x = arctan(√3 / 3) + π/5
Therefore, the solution to the equation 3tan(x - π/5) - √3 = 0 is:
x = arctan(√3 / 3) + π/5
To solve the equation 3tan(x - π/5) - √3 = 0, we will follow these steps:
Step 1: Add √3 to both sides to isolate the term with the tangent function:
3tan(x - π/5) = √3
Step 2: Divide both sides by 3 to solve for the tangent expression:
tan(x - π/5) = √3/3
Step 3: Take the inverse tangent (arctan) of both sides to find x - π/5:
x - π/5 = arctan(√3/3)
Step 4: Add π/5 to both sides to solve for x:
x = arctan(√3/3) + π/5
Hence, the solution to the equation 3tan(x - π/5) - √3 = 0 is x = arctan(√3/3) + π/5.