1. 1.6 Trig Functions
Greg Kelly, Hanford High School, Richland, Washington

2. 1.6 Trig Functions
The Mean Streak, Cedar Point Amusement Park, Sandusky, OH

3. Trigonometric functions are used extensively in calculus.
When you use trig functions in calculus, you must use radian measure for the angles. The best plan is to set the calculator mode to radians and use when you need to use degrees.
2nd o
If you want to brush up on trig functions, they are graphed on page 41.

4. 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 doesn’t change.
Cosine is an even function because:
Secant is also an even function, because it is the reciprocal of cosine.
Even functions are symmetric about the y - axis.

5. 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.
Sine is an odd function because:
Cosecant, tangent and cotangent are also odd, because their formulas contain the sine function.
Odd functions have origin symmetry.

6. 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.
is a stretch.
Horizontal shift
Horizontal stretch or shrink;
reflection about y-axis
Positive c moves left.
is a shrink.
The horizontal changes happen in the opposite direction to what you might expect.

7. When we apply these rules to sine and cosine, we use some different terms.
is the amplitude.
Vertical shift
is the period.
Horizontal shift B A C D

8. 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.

9. Tuning Fork Data
Time:
Pressure:
2nd {
.00108,.00198,.00289,.00379,.00471
2nd }
STO
alpha
L 1
ENTER 6 3 9
alpha
L 1 ,
alpha
L 2
ENTER
2nd
MATH
SinReg
The calculator should return:
Statistics
Regressions
Done

10. 6 3 9
alpha
L 1 ,
alpha
L 2
ENTER
2nd
MATH
SinReg
The calculator should return:
Statistics
Regressions
Done 6 8
ENTER
2nd
MATH
Statistics
ShowStat
The calculator gives you an equation and constants:

11. We can use the calculator to plot the new curve along with the original points:Y=
y1=regeq(x) x )
regeq
2nd
VAR-LINK
Plot 1
ENTER
ENTER
WINDOW

12. Plot 1
ENTER
ENTER
WINDOW
GRAPH

13. WINDOW
GRAPH
You could use the “trace” function to investigate the pressure at any given time.

14. p 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