Section+1.9A

Here are the notes from Friday, September 2, 2011

Proper Notation:

This is the proper notation for expressing all solutions to a problem involving the tangent function, because when looking at the graph you can see that as the period is the answers will be the same when is multiplied by an integer.

This is the proper notation for expressing all solutions to a problem involving the cosine function. It is similar to that of tangent, except that the period is 2 instead of . However, because there are two answers very near to each other on the graph, there are two ways to find x. Here's the other one:



[Mrs. Tyson is editting this page to add that the paragraph below is not correct about general solutions to sin(x) equations] This is the proper notation for expressing all solutions to a problem involving the sine function, which is similar to that of tangent, but the first value must be negated, because you have to subtract it from pi to get the correct answer.

will always equal the function inverse, not the multiplicative inverse in class, because the multiplicative is, or

The calculator will give us different answers then we might expect. For example, one might expect that would equal or . However, the calculator will always restrict the range of the function and give you an answer that is or [Mrs. Tyson is editting to add that this is not the right range for sine inverse]. This means that if you are expecting an answer that is not in the first quadrant, you will get one that is in the fourth quadrant, but is the equivalent of the negated version of the answer in the first quadrant. [However, this sentence is correct]