another solving trigonometry equation?

Question

solve each equation for principal values of x. express solutions in degrees.

tan2x - square root of 3 = 0

when i work this out, i get tanx= square root of 3 divided by 2 but none of these are on the unit circle

Answer 1

Hi,

If you add square root of three, you get:

tan2x = square root of 3 This as a fraction is sqrt(3)/1. The sqrt(3)/1 are the 2 legs of a 30-60-90 triangle, where the angle across from the sqrt(3) is a 60 degree reference angle.

Since the tangent value is positive, it could be in the first or third quadrants. When tan(2x) = sqrt(3)/1 then 2x = 60 in the first quadrant or 2x = 240 in the third quadrant. Solving these for x, x could equal either 30 or 120 degrees.

I hope that helps.

Answer 2

You can't take the "2" out of the Tangent function and divide with it. The first principal value is 30 degrees, since 2x=60, for which Tan 60=sqrt(3).

Answer 3

You cannot take out the from tan(2x). The 2 inside the function of tan(2x) is not multiplying the function itself, it's multiplying the ARGUMENT of the function. Look at this example:

f(2x) = x^2

For x = 3:

f(2 * 3) = (2.3)^2
f(6) = 6^2
f(6) = 36

If you see the 2 inside the function never multiplied the function itself, but it did multiply the argument.

In other words f(2x) and 2f(x) is not the same thing.

With tan(2x) is the same thing. So if you want to resolve for x you have to do this:

tan(2x) = 3^1/2
arctan(tan(2x)) = arctan(3^1/2)===> arctan(x) is the inverse of tan(x). So?\:

2x = arctan(3^1/2)
x = arctan(3^1/2)/2
x = pi/6

Answer 4

you cant divide the 2 out of tan(2x)


Tan(2x)=(2Tan(x))/(1-Tan(x)^2)

that might help you if you do a bit more work on it