why does tan(-120) = - 0.71312301
and not sqrt 3 ?
I tried making a graph and still came up with sqrt 3??
so what would 0.71312301 be as a sqrt?
tan -120 = (sqrt(3)) = 1.73205
coterminal with 240 deg in QIII so positive
reference angle is 60
Where did you get - 0.71312301
Are you using a cal. set to the wrong setting, rads vs degrees?
I used a calculator to check my answer, (which was originally sqrt 3) and then on the calculator I got 0.713... so I was confused ... anyway thank you
also, for even vs. odd functions it saids that tan(-angle) = - tan(angle)
so that doesn't matter since tan is positive in the QIII?
The value of tan(-120) is indeed -0.71312301, not sqrt(3), because when referencing trigonometric functions like tangent, we need to consider the unit circle and the range of the function.
To understand why tan(-120) is -0.71312301, let's start by considering the unit circle. The unit circle is a circle centered at the origin (0,0) with a radius of 1. It is used to represent trigonometric functions and their values for different angles.
To find the value of tan(-120), we need to locate the angle -120 degrees on the unit circle. Starting from the positive x-axis (angle 0 degrees), we rotate clockwise by 120 degrees. In this position, we end up in the fourth quadrant.
In the fourth quadrant, the tan function is negative. Therefore, we know that tan(-120) will be negative.
Next, we can determine the value of tan(-120) by drawing a vertical line from the point on the unit circle corresponding to -120 degrees to the x-axis. The intersection point gives us the y-coordinate, while the x-coordinate is 1 (since the point lies on the unit circle).
In this case, the y-coordinate is approximately -0.866 (rounded value).
Now, we can calculate the ratio of the y-coordinate to the x-coordinate: -0.866/1 = -0.866.
Thus, tan(-120) is approximately -0.866 or -0.71312301 (more precise decimal value).
It is important to note that sqrt(3) is the value of tan(60) in the first quadrant. The angles -120 and 60 degrees are supplementary angles, meaning that they sum up to 180 degrees. While they have a relationship, they do not have the same trigonometric values.
Therefore, when calculating tan(-120), it is necessary to consider the position of the angle on the unit circle, the quadrant, and the range of the tangent function.