Inverse Trigonometric Functions—Section 6.6—Day 1
We use inverse trig functions to find missing angles when we have
ratios of sides. But we have a significant problem! Because each
trigonometric function repeats, NONE OF THEM PASS THE
HORIZONTAL LINE TEST!
See page 553 of your book for the definition.
Here is a graph of the inverse sine AND WHERE IT CAME FROM:
The inverse cosine is defined on page 556. Here is a graph of the inverse cosine:
The inverse tangent is defined on page 557. Here is a graph of the inverse tangent:
You really can learn and remember the name, notation, domain
and range of each function. Your teacher used the graphs above
and the table below when she learned these.
Name
Inverse sine
Inverse cosine
Inverse
tangent
Notation
sin-1(x) or
arcsin(x)
cos-1(x) or
arccos(x)
tan-1(x) or
arctan(x)
Domain
Range
New today: We can find the angles in a right
triangle:

These should all be the same.
Advice: Use the book, study plan and assigned problems until you know how to
use your calculator quickly to find inverse trigonometric functions, until you learn
the restrictions on the inverse trig functions, and until you can solve right triangles
for both sides and angles.
GOAL: Memorize the names, notation, domains and ranges of inverse
trigonometric functions and solve right triangles for missing angles. (We will
solve equations tomorrow.)