11 - Learn ArcSin, ArcCos & ArcTan (Inverse Sin, Cos & Tan) - Part 1
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- เผยแพร่เมื่อ 1 ก.ค. 2024
- View more at www.MathAndScience.com. In this lesson, you will learn how to use the arcsin, arccos, and arctan functions. These functions are also known as inverse sin, inverse cos, and inverse tan. The purpose of these inverse functions is to calculate the angle required to produce a given sin, cos, or tan. In other words, these are the opposite functions to sin(x), cos(x) and tan(x). They are used in all branches of math, science, physics, and engineering because we frequently need to calculate the angle required for a given system to function properly. There are several important things to understand about these functions, and we will discuss all of the ways to use them and understand what angles are allowed to be returned by each of these functions. In other words, will discuss the domain and range of the arcsin, arccos, and arctan functions.
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Great video on trigonometry. Always a tricky subject for students.
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This was very helpful! I'm working my way through a book right now that's all derivations of inverse trig functions and it's maddening. Like where the hypotenuse is 1, another side is x, and the third side is the square root of 1-xsquared. So a lot of it is going back to previous identities (like angle sum and diff). This video definitely helped me compartmentalize all that in my head a lot better so, thank you. If you have any other videos on inverse trig functions and I'm just not seeing them, please let me know!
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@@MathAndScience here India for jee it's in class 11 only
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Wouldn't it be advisable to indicate that the solution of the ArcSin, for example, lead the solution with a notation that it is an angle. Such as a angle symbol. Avoid the mistake that it not be recognized as an angle solution.
At 6.20 in the case of arc tan.. The input should be -inf to +inf but on the board it is -1 to +1
You can make a timestamp by using the colon mark .
like this 6:20
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What about angles that aren’t perfect on the unit circle? How can we calculate that without punching it into the calculator and getting an answer? Like arcsin of 4/7?
BINGO. It's all just chart memorization...
For an inverse function to be defined, there should be only one unique out for each input. Eg sinπ/6=1/2 and sin5π/6=1/2, these have same the output. Hence no inverse function in the 2nd quadrant. Similarly with the 3rd and 4th quadrant.Right?
Is (sinx)^-2=1/sin^2 ?
We prefix inverse functions with arc . Does it mean, it refers to some particular portion of the unit circle rather than entire circumference?
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Yes it’s tricky. I advise to watch this lesson several times to absorb it all. The bottom line is that for ArcSin to be a 1-to-1 function, we must restrict the angles it can return. If we didn’t do that then it couldn’t be a function at all. So yes they are functions after all!
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Where is this used in real life? Serious question no joke
In Calc class
@35:35 isn't Tan(+/- pi/2) broken at this point?
Yes... it shows Error on my calculator then begins anew.
so its like= what division is to multiplication= what arcsin is to sin... wow thanks.
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