tan(2theta-34degrees)=squareroot3, theta range{real numbers of degrees}
tan(2θ-34) = √3
means that 2θ-34 = 180k + 60 for any integer k
θ = (90k + 47)°
So:
47
137
227
317
Do I need to add +360n?
To solve the equation tan(2theta - 34 degrees) = √3 for theta, we can follow these steps:
Step 1: Transform the equation
We need to isolate theta, so let's work towards that by transforming the equation. First, let's take the inverse tangent (tan^-1) of both sides:
tan^-1(tan(2theta - 34 degrees)) = tan^-1(√3)
Since tan^-1(tan(x)) = x for any real number x, the left side simplifies to:
2theta - 34 degrees = tan^-1(√3)
Step 2: Solve for theta
Now, we can isolate theta by adding 34 degrees to both sides of the equation:
2theta - 34 degrees + 34 degrees = tan^-1(√3) + 34 degrees
Simplifying further:
2theta = tan^-1(√3) + 34 degrees
Finally, divide both sides of the equation by 2 to solve for theta:
theta = (tan^-1(√3) + 34 degrees) / 2
Therefore, the solution for theta, within the given range of real numbers of degrees, is:
theta = (tan^-1(√3) + 34 degrees) / 2