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# Using inverse trig functions with a calculator

Sal discusses the appropriate way to use the calculator in order to find an angle when its tangent value is given. Created by Sal Khan.

## Want to join the conversation?

• If the restrictions for tan are the quadrants I and IV. Why would we need more information to solve?
• The restrictions for the inverse function of tan, the arctan, are quadrants 1 and 4. These restrictions do not apply to the original tan function. Since the question stated tan(x)=1, assuming that the value of x is restricted to -pi<x<pi would potentially remove some answers that could have been the actual value of x.

This is similar to when you take the square root of an equation on both sides e.g. (x^2 = 4) to solve for x, but neglect the value of -2 that would also be a solution to the equation. You're essentially ignoring answers that exist. Hope I helped :)
• The question does not seem specific enough to answer unambiguously.
• Couldn't options C and D also be considered as answers, because the inverse tangent function will get us the answer of the ø in the first quadrant while the C option will give the second angle which in this case is in the 3rd Quadrant. So, using options C and D, we are practically able to figure out both the angles and of-course we can add or subtract 2π to get all the possible angles. So, why is the answer option B?
• `C` is defined as `pi - atan(θ)`, this would put you into `QII`, not `QIII`. If C said `pi + atan(θ)`, then you would be in `QIII`. `D` would give the right slope and angle, but the fact remains that you have an ambiguous state that makes the choice `B` for more information the best answer.
• At , how do you know the slope of the tangent is one?
• It is given that tan θ = 1 in the problem.
• I think the big problem I am having with khan now, is that there are so so so many gaps in what is taught.
You teach how to solve the equations but none of the theory, and for someone with no math background, that is like building a house of cards with mere slices of the cards.
• I'm having the same problem. I am an adult learner aiming to go back to school this fall and started doing Khan in order to start at a higher level math.
KA claims to be the way to go to "master" the subjects but as I've gone further through the high school math courses here, I've found that to not be the case. Like you said, so many gaps so I had to look elsewhere. Eddie Woo's youtube channel has helped me tremendously on gaining a full understanding but you have to search his channel for the topics you want. He has playlists as well, here's one someone created about trig that I've found to be really good: www.youtube.com/playlist?list=PLYb4IXcMLZTJfLeV_rqqsSsWJaa_YK_7Z

I'd be interested in hearing how you're doing now, 4 months later
• But the question said select all that apply, so dosen't that mean that both get more information and type arctan(1) into his calculator should work?
• it really depends on the situation, you can't just type in arctan(1) without knowing more because that would make pi-arctan(1) also a valid choice. Since both of these options give two different angles we will need more information in order to choose between them.
• Why when I type tan^-1 of some really large quantity in the calculator it write 90 ? shouldn't it never reach 90 ?
• The limit of the function arctan(x) is pi/2 or 90 degrees as you go towards infinity (from the left).
So while you never actually get to 90 degrees you get so close that there's barely any difference.
But yes you're right you'll never actually reach 90 degrees, your calculator just rounds to 90 degrees (something like 89.9999999999999999999 becomes 90).

• Is it normal for a TI-84 Plus calculator to give inaccurate answers/not run programs properly when its battery is low?
• If your calculator is giving incorrect values, make sure that it is in either radian or degree mode. (Whichever one the measurements are taken in.) This could be the cause of your calculator giving incorrect values. (To check, go to mode and make sure that the unit you want to use is highlighted.)
• Wait, what should be the Javier's answer?