If tanθ = -√3, then θ = tan(inverse) -√3, It is equal to -60º or 120º Why???? Please give reason?

Answer 1

tan is negative in the second and fourth quadrant, so both answers are correct.

-60 is in the fourth quadrant
120 is in the second quadrant

You didn't give a domain, so both answers are correct. If you were told the answer had to be between 0 and 180, for example, then 120 is correct (because -60 is NOT between 0 and 180).

Answer 2

Inverse Tangent Of 3

Answer 3

With a 60 degree angle:
y = √3
x = 1
r = 2

So at 60 degrees, tanθ = y/x = √3

But 120 degrees is in the second quadrant, where x is negative and y is positive.

180 degrees minus 120 degrees is 60 degrees, and in the second quadrant. Do you see that you need to subtract 120 degrees from 180 degrees since it is in the second quadrant?

So at -60 degrees, tanθ = y/x = √3/(-1) = -√3

Answer 4

The tangent of an angle is the ratio of the length of the opposite side divided by the length of the adjacent side. Now, if the tan of θ is -√3, that means that either the opposite side must be negative and the adjacent side positive, or vice-versa. (If they were both positive or both negative, then the ratio would be √3, not -√3...get it?)

So, if the opposite is positive and the adjacent negative, then the angle must be in the 2nd quadrant, and the answer is 120º. If the opposite is negative and the adjacent is positive, then the angle must be in the 4th quadrant and the answer is -60º. So, both answers are correct.

Answer 5

As you increase (or decrease) the value of your angle, the value of the tangent goes through a cycle shown in http://www1.chapman.edu/~jipsen/svg/curves/trigtan.html or in http://www.graphnow.com/details/trigonometric-functions.html (2nd drawing). Thus you can come at the same point on the tangent-value cycle from two different directions. As a result, either −60° or +120° will have a tangent of −√3, as shown in http://library.thinkquest.org/C0110248/trigonometry/ratio_negative.htm and http://library.thinkquest.org/C0110248/trigonometry/ratio_general2.htm . So arctan −√3, the angle that gives a tangent of −√3, has two values. (Actually it has as many values as the number of times you add or subtract 360° to the angle, but here we assume you never add/subtract more than 359°.)

Answer 6

Obviously lamb with be proportionally smaller but it would still support quadratic equation to give 4 big bits of Pi. Its all theoretically relative, therefore - Pi equals Theory of relativity (but only on a sunday).

Answer 7

If no domain was given then both are correct, and if you know what the graph of tanθ looks like, you can see how the graph repeats. So technically if you keep adding 180º, θ can equal 300º , 480º , 660º ... if there was no domain since it repeats forever.