Chapter 8

-Simple Trigonometric Functions
-Sine and Cosine Curves

This week we learned the beginning of chapter 8. In chapter 8 we learned inverses of trigonometric functions. In section 8-2 we learned properties of the curves of sine and cosine (amplitudes, periods), and how to graph them.
Section 8.1
Finding the inverse.

Ex.
3Cosx=1
*Make sure that your calculator is in DEGREES, not radians. You WILL get the wrong answer.

Like any equation, you must get the variable by itself in order to solve. So first divide “cosx’ by 3.
- 3cosx/3 = 1/3
Next, you have to solve for x. X will equal the inverse of cosine.
X=Cos^-1(1/3)
Finally, you calculate (enter into your calculator) the inverse of cosine of (1/3).
Your answer should be 70.528 degrees. Round to the nearest tenth of a degree if not stated.
X=70.5°

Section 8-2
Amplitudes and Periods
The Amplitude of a periodic function is the point in which the function reaches its maximum height.
The period of a function is how long it takes a function takes to repeat itself.
For the functions: Y= A sine Bx
Y= A cos Bx
Amplitude equals the absolute value of A.
Ex. Y=2 sine 3x
The amplitude = absolute value of l 2 l which is 2, therefore Amplitude= 2.
In order to find the period, you must use the formula 2π/B.
The period equals 2 π/3