Calculus 1.6

1
Trig Functions
Black Canyon of the Gunnison National Park,
Colorado
2
Trigonometric functions are used extensively in
calculus.
If you want to brush up on trig functions, they
are graphed in your book.
3
Even and Odd Trig Functions
Even functions behave like polynomials with
even exponents, in that when you change the sign
of x, the y value doesnt change.
Secant is also an even function, because it is
the reciprocal of cosine.
Even functions are symmetric about the y - axis.
4
Even and Odd Trig Functions
Odd functions behave like polynomials with odd
exponents, in that when you change the sign of x,
the sign of the y value also changes.
Cosecant, tangent and cotangent are also odd,
because their formulas contain the sine function.
Odd functions have origin symmetry.
5
The rules for shifting, stretching, shrinking,
and reflecting the graph of a function apply to
trigonometric functions.
Vertical stretch or shrink reflection about
x-axis
Vertical shift
Positive d moves up.
Horizontal shift
Horizontal stretch or shrink reflection about
y-axis
Positive c moves left.
The horizontal changes happen in the opposite
direction to what you might expect.
6
When we apply these rules to sine and cosine, we
use some different terms.
Vertical shift
Horizontal shift
7
Trig functions are not one-to-one.
However, the domain can be restricted for trig
functions to make them one-to-one.
These restricted trig functions have inverses.
Inverse trig functions and their restricted
domains and ranges are defined in the book.
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