We continue practicing the graphs of the six trigonometric functions and all of
their variations. This week we will graph combinations of the trigonometric
functions, combinations of algebraic and trigonometric functions, and
some inverse trigonometric functions.
for sine and cosine (and then for tangent, cotangent, secant, and
cosecant as well), we have learned the "framing box" that we "hang"
our function "in" or "on".
focus on the key points for each of the six functions
the handouts on our website explain these ideas visually
So far, given any angle, we can state the values of all six trigonometric
functions for that angle, but we would also like to do the reverse. If we know
the values of the six trigonometric functions for an angle, or if we are given
just one trigonometric value, we want to be able to name the angle, or angles,
with that value. This ability is also built into your calculator under the
inverse trigonometric functions.
The inverse trigonometric functions should not be confused with the reciprocal
functions (though the notation can be confusing at first). Since the
trigonometric functions repeat their values over and over again (that's why we
call them periodic), we begin by assigning a particular angle with each
trigonometric value, what we call the principal angle.
Each inverse trigonometric function has a rule for selecting principal angles
and we call that rule the principal domain of the inverse trigonometric
function. It is important to understand that your calculator always and
only selects the principal angle when you use an inverse trigonometric
function.
We are at an important point in the course, just about the halfway point. By the
end of next week you have have completed half of your coursework (homework, quizzes,
and exams).
You are in the middle of the work and that makes it challenging to see the whole
picture. To this point you have been learning facts about trigonometry, and
in the second half of the course you are going to learn more about what to do
with trigonometry.