Hint: SOHCAHTOA Warm Up Solve for x:

Slides:



Advertisements
Similar presentations
Solving Radical Equations and Inequalities 8-8
Advertisements

10.5 Write Trigonometric Functions and Models What is a sinusoid? How do you write a function for a sinusoid? How do you model a situation with a circular.
EXAMPLE 1 Solve a multi-step problem
Periodic Functions by: Doris Santarone.
4.5 Sinusoidal Graphs Sketching and Writing Equations.
Translations of sine and cosine graphs The graph will be shifted to the right by c. The graph will be shifted up d. We already know what A and B are used.
Example 1-3a ALGEBRA Solve Write the equation. Take the square root of each side. The equation has two solutions, Answer: Notice that.
Quadratic formula.
Practice for tomorrow’s test (solutions included).
10.2 Translate and Reflect Trigonometric Graphs
Sinusoidal Functions Topic 1: Graphs of Sinusoidal Functions.
5-9 Operations with Complex Numbers Warm Up Lesson Presentation
EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3.
Multiplying Fractions 5 th Grade Mrs. Mitchell. Vocabulary Week 1 Numerator - the number above the line in a fraction (the number on top) that shows how.
Warm-Up Change each decimal to a fraction:
Algebra 2B - Chapter 6 Quadratic Functions. 6-1: Graphing Quadratic Functions Learning Targets: I can graph quadratics using five points. I can find max.
Physics Type 2 Projectile Motion Type 3 Projectile Motion
Today in Precalculus Turn in graded worksheet Notes: Simulating circular motion – Ferris Wheels Homework.
Graphs of Sine and Cosine
Express each number in terms of i.
EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3. SOLUTION STEP 1 Identify the amplitude, period, horizontal shift, and vertical shift. Amplitude:
Title of Lesson: Quadratics Pages in Text Any Relevant Graphics or Videos.
4.5 “Square Roots”. More Examples Rationalizing the Denominator.
Translations of Trigonometric Graphs LESSON 12–8.
Solving Equations with Trig Functions. Labeling a right triangle A.
Graphing Rational Functions Day 3. Graph with 2 Vertical Asymptotes Step 1Factor:
Chapter 6 Section 6.3 Graphs of Sine and Cosine Functions.
6-6. “A” is for amplitude. This is ½ the distance from the highest and lowest value. So……. Highest Value – Lowest Value 2.
MCR 3U Final Exam Review: Trigonometric Functions Special Angles.
Splash Screen.
y = | a | • f (x) by horizontal and vertical translations
Unit 7 Trigonometric Graphs Review Problems
Splash Screen.
Solve Quadratic Equations by Finding Square Roots
2.7 Sinusoidal Graphs; Curve Fitting
Collect Interims and test corrections!
Operations with Complex Numbers
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
Periodic Functions by: Doris Santarone.
Ferris Wheel.
Warm Up Solve for x:
Objectives: Students will learn how to find Cos, Sin & Tan using the special right triangles.
Graphs of Trig Functions
Solving Trig Functions
Applications of Sinusoidal Functions
Warm-up 1)Simplify and leave in simplest radical form: 2) The function y = 14,000(0.8)x represents the value of a car x years after purchase. Find the.
Warm-up Unit 3 Day 4 How do you graph a line?
Splash Screen.
Collect test corrections!
Warm-up  .
I can write trig functions from a graph
Objective: To solve systems of second degree equations
M3U7D3 Warm Up Shifted up one Stretched by 3 times
6-4 Circles Warm Up Problem of the Day Lesson Presentation Pre-Algebra.
Section 3.3 Graphing Sine Cosine and Tangent Functions
Warm Up Use your unit circle to find the exact value:
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.
5 minutes Warm-Up Solve. 1) 2) 3) 4).
Drawing Trigonometric Graphs.
On the unit circle, which radian measure represents the point located at (− 1 2 , − 3 2 )? What about at ( 2 2 , − 2 2 )? Problem of the Day.
Section 8.3 Part 2 Slope and y-intercept pages
Graph Proportional Relationships
A. Determine any asymptotes, holes, and intercepts of
GRAPHS OF SINE AND COSINE
Graphing: Sine and Cosine
Complete each table. Students,
Graphing Trig. Functions
Algebra 1 Warm Ups 9/25 - 9/28.
L13. 1 and L13. 2 Obj 1: Students will find period and amplitude
13-1: Exploring Periodic Data
Presentation transcript:

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