1. Hint: SOHCAHTOA Warm Up Solve for x: 𝟏𝟐 𝒙 𝟒 𝟑 =𝟏𝟗𝟐 𝒄𝒐𝒔 𝟖𝟓 =𝒙
I can graph the sine function
Warm Up
Solve for x:
𝟏𝟐 𝒙 𝟒 𝟑 =𝟏𝟗𝟐
𝒄𝒐𝒔 𝟖𝟓 =𝒙
𝒔𝒊𝒏 𝟒𝟐 = 𝒙 𝟐
Hint:
SOHCAHTOA 15
30° 𝑥

2. Warm Up
Solve for x:
𝟏𝟐 𝒙 𝟒 𝟑 =𝟏𝟗𝟐
𝒄𝒐𝒔 𝟖𝟓 =𝒙

3. Warm Up
Solve for x:
𝒔𝒊𝒏 𝟒𝟐 = 𝒙 𝟐 d) 15
30° 𝑥

4. Homework vs Grade Tests Learning Targets Homework Final Grade 67% 76%
56% D
66%
79%
43%
64%
75%
71% C
83%
96%
100% A
74%
89%
38% C C D B B

5. Periodic Functions
Periodic Function: A continuing function with x and y values that repeat periodically

6. Periodic Functions Real-World examples A day (24 hours long, repeats)
The path of the earth as it circles the sun
Tides

7. The Screamer
The newest ride at a local amusement park is The Screamer. It is an enormous wheel with a radius of 100 feet. Half of the wheel is below ground level, in a very dark, murky pit with water at the bottom. As The Screamer rotates at dizzying speeds, riders fly up into the air before plunging downward through blasts of freezing air, hair-raising screams, and sticky spider webs into the pit where they splash through the dark, eerie water on their way back above ground. The ride rotates 15° to load and unload the next set of riders.

8. The Screamer

9. The Screamer Degree Height 0° 15° 25.88 30° 50 45° 70.71 60° 86.60 75°
100
60° 𝑥 0°
100
45°
70.71
15°
25.88
100
30° 50
100
15°
25.88
30° 50
45°
70.71
60°
86.60
75°
96.59
90°
100
sin 60 = 𝑥 100
.8660= 𝑥 100
𝑥=86.60

10. Sine Function – Complete the Table
Working in table groups, complete the table Do you notice a pattern? Graph the function where 𝑥 is the degree and 𝑦 is the height off the ground

11. Sine Function - Graph
100
−100

12. Periodic Functions Vocabulary
Period: The horizontal length of one complete repetition of the pattern of the function
Period

13. Periodic Functions Vocabulary
Midline: the horizontal axis about which the periodic function oscillates
Midline

14. Periodic Functions Vocabulary
Amplitude: distance from the midline to the max/min of the periodic function
𝑨= 𝟏 𝟐 𝒎𝒂𝒙−𝒎𝒊𝒏
Amplitude

15. Break!

16. Rationalizing the Denominator
What is a rational number? What is an irrational number? What is a denominator? What does it mean to rationalize the denominator?

17. Rationalizing the Denominator
Steps 1) Multiply the top and bottom by radical in the denominator
Example
( ) 3
( ) 3

18. Rationalizing the Denominator
Steps
Multiply the top and bottom by radical in the denominator
Reduce
Example
( ) 5
( ) 5

19. Check your answers on the back table
Review Practice
10 minutes
Check your answers on the back table

20. Anything not finished is homework
Textbook:
8-5 through 8-11
Anything not finished is homework

21. Unit Circle
Solve for 𝑥
sin 30 =𝑥
𝑥= 1 2
60° 1 𝑥
30° 𝑦

22. Unit Circle Solve for 𝑥 sin 45 =𝑥 𝑥=.70710678 𝑥 𝑦 𝑥 1
Is there another way to solve for 𝑥?
𝑥 2 + 𝑦 2 = 1 2
𝑥 2 + 𝑥 2 =1
Type equation here.
45° 1 𝑥
45° 𝑦 𝑥