1. U8P2D6 Have out: Bellwork:
Pencil, red pen, highlighter, assignment, calculator
Bellwork:
Graph one positive period of each function. Using radians, and be sure label the axes. y x
+2 y1 5 +1
|a| = ____ 5 y1
b = ____ 4 +1
+2 y2 +1 y2
p = ____ +1
h = ____
To the left
+2 labeled x–axis
+1 scale –5
total:
+1 labeled y–axis

2. Identify and/or describe the major parts of the function
y = a sin (b (x – h)) + k
Amplitude
|a| = ________________
b = ________________
Horizontal Shift
Frequency
Vertical Shift
b = ________________
p = ________________
Period
p = ________________

3. Is there a “sine” name for ? ________________
Sketch one period for each pair of functions on the same axes. Use radian measure. y 2 2 . . x
Is there a “sine” name for
? ________________

4. Is there a “cosine” name for ? ________________y 3 3 . . x
Is there a “cosine” name for
? ________________

5. Is there a simple name for ? ________________y 4 4 . . x
Is there a simple name for
? ________________

6. Is there a “cosine” name for ? ________________y . . x
Is there a “cosine” name for
? ________________

7. Work on the practice.

8. Old Slides

9. Solving Trigonometric Equations
Trigonometric equations can be solved by using methods from algebra.
Example #1:
Solve for x.
Solve for all values of θ between 0 ≤ θ < 2π. y x 1 4 4 4 4 θ
θ =

10. Example #2:
Solve for x.
Solve for all values of θ between 0 ≤ θ < 2π. y x
(0, 1)
x = 0
x + 1 = 0
(–1, 0) θ
x = –1
(0, –1)
θ =

11. Example #3:
Solve for x.
Solve for all values of θ between 0 ≤ θ < 2π. y x
3x3 = x
3x3 – x = 0
(1, 0)
(–1, 0)
x(3x2 – 1) = 0
x = 0
3x2 – 1 = 0
θ = 0,
3x2 = 1 y x 2 1 θ
θ =

12. Example #4:
Solve for x and y.
Solve for all values of θ between 0 ≤ θ < 2π. y x
2xy – x = 0
x(2y – 1) = 0
(1, 0)
(–1, 0)
x = 0
2y – 1 = 0
2y = 1
θ = 0, y x 1 θ
θ =

13. Example #5:
Solve for x.
Solve for all values of θ between 0 ≤ θ < 2π. y x
2x2 + 3x + 1 = 0 2 3 2 1
(–1, 0) x
+ 1
θ = 2x
2x2 2x 1x 1 y x
+ 1 1
(x + 1)(2x + 1) = 0 θ
x + 1 = 0
2x + 1 = 0
x = –1
2x = –1
θ =