This lecture covers the computations of inverse trigonometric functions. You'll learn the values of the inverse trig functions for some special angles, using the unit circle. It is important to know where these inverse functions are defined and where their answers lie. The domain of the sine is the range of the arcsine, while the range of the sine is the domain of the arcsine. This applies for the other two as well. You'll also learn which of these functions is even, which is odd and which is neither. This could be determined from both the graph and the equation of the function.
*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Computations of Inverse Trigonometric Functions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
This problem is really kind of testing whether you know the graphs of arcsin, arccos, and arctan look like.0675
If you don't remember those, then you go back to sine, cosine and tangent, and you snip off the important pieces of those graphs, and you flip them around y=x to get the graphs of arcsin, arccos, and arctan.0685
Those are the graphs that I have in blue here, arcsin, arccos, and arctan.0700
The other thing that this problem is really testing is whether you remember the graphical characterizations of odd and even functions.0705
If you know that odd functions have rotational symmetry around the origin, even functions have mirror symmetry across the y-axis, it's easy to check these graphs to just look at them and see whether they have the right kind of symmetry.0717
Of course, what you find out is that arcsin(x) has rotational symmetry, arccos(x) doesn't have either one, arctan(x) also has rotational symmetry.0732
For our third example here, we're trying to find arccos of the following list of common values.0746
Again, it's useful to start with a unit circle here.0753
Once you start with a unit circle, remember that with arccos, you're looking for values between 0 and π.0766