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

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

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

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

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

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

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.

The Screamer

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

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

Sine Function - Graph 100 −100

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

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

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

Break!

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?

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

Rationalizing the Denominator Steps Multiply the top and bottom by radical in the denominator Reduce Example 2 15 5 15 5 5 3 5 ( ) 5 ( ) 5

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

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

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

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