Calculus 1.6

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1.6 Trig Functions
Greg Kelly, Hanford High School, Richland,
Washington
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1.6 Trig Functions
The Mean Streak, Cedar Point Amusement Park,
Sandusky, OH
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Trigonometric functions are used extensively in
calculus.
If you want to brush up on trig functions, they
are graphed on page 41.
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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.
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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.
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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.
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When we apply these rules to sine and cosine, we
use some different terms.
Vertical shift
Horizontal shift
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The sine equation is built into the TI-89 as a
sinusoidal regression equation.
For practice, we will find the sinusoidal
equation for the tuning fork data on page 45. To
save time, we will use only five points instead
of all the data.
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Tuning Fork Data
Time .00108 .00198 .00289
.00379 .00471 Pressure .200
.771 -.309 .480 .581
.00108,.00198,.00289,.00379,.00471
2nd

2nd

alpha
L 1
6
3
9
alpha
L 1
alpha
L 2
,
2nd
MATH
SinReg
The calculator should return
Statistics
Regressions
Done
10
6
3
9
alpha
L 1
alpha
L 2
,
2nd
MATH
SinReg
The calculator should return
Statistics
Regressions
Done
6
8
2nd
MATH
Statistics
ShowStat
The calculator gives you an equation and
constants
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We can use the calculator to plot the new curve
along with the original points
x
y1regeq(x)
)
regeq
2nd
VAR-LINK
Plot 1
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Plot 1
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You could use the trace function to investigate
the pressure at any given time.
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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 on page 47.
p