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Current time:0:00Total duration:3:35

Using inverse trig functions with a calculator

Video transcript

Xavier is calibrating sophisticated medical imaging equipment the manual reports that the tangent of a particular angle is one so that's saying that the tangent let's say that that particular angle is theta is equal to one what should Javier do to find the angle and I encourage you to pause this video and look at these choices and think about which of these should he do to find the angle so let's look through each of them so the first one well actually instead of looking the choices let's think about what we would do to find the angle so this thing that the tangent of some angle is equal to one well one thing that you might want to do is say okay let's just say if we take the inverse tangent if we take the inverse tangent of the tangent of theta so if we take the inverse tangent of both sides of this we of course would get the inverse tangent of the tangent of theta if the domain over here is restricted appropriately is just going to be equal to theta so that we can say the tangent the theta is going to be the inverse tangent of one so it might be tempting to just pick this one right over here type inverse tangent of one into his calculator so maybe maybe this looks like this looks like the best choice but remember I said if we restrict the domain right over here if we restrict the possible values of tangent of theta here appropriately then this is going to simplify to this but there is a scenario where this does not happen and that's as if we pick Thetas that are outside of the range of the inverse tangent function now what do I mean by that what's really just based on the idea that there's multiple angles that have there are multiple angles whose tangent is one and let me draw that here with a unit circle here so when you draw a unit circle so it's my x-axis that's my y-axis let me draw my unit circle here make sure you probably don't even have to draw the unit circle because the tangent is really much more about the slope of the Ray created by the angle then where it intersects the unit circle as would be the case with sine and cosine so if you have so you could have this angle right over here so let's say this is a candidate theta where the tangent of this theta is the slope of this line and this terminal angle I guess you there terminal ray you could say of the angle the other side the initial ray is along the positive x axis and so you could say okay the tangent of this theta tangent of this theta is 1 because the slope of this line is 1 let me scroll over a little bit well so let me write it this way so tangent theta is equal to 1 but I can construct another theta whose tangent is equal to 1 by going all the way over here and essentially going in the opposite direction but the slope of this line so let's call this theta - tangent of theta 2 is also going to be equal to 1 and of course you could go down you could go another PI radians and go back to the original angle but those are fun that's functionally the same angle in terms of in terms of how where it is relative to the positive x-axis or what direction it points in to but this one is fundamentally a different angle so we do not know we do not have enough information just given what we've been told to know exactly which theta we're talking about whether we're talking about this orange theta or this mole data so I would say to get more information there are multiple angles which fit this description