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# Trigonometry 2014/15

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## Rick Hollenbeck

on 12 May 2017

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#### Transcript of Trigonometry 2014/15

August 25th, 26th
Objective: Students will understand how to use similarity criteria to solve problems in geometric figures
Hint:
How would your answer change if the side of the square was 20 units?
August 27th
Objective: Students will understand how to use similarity criteria to solve problems in geometric figures
How many triangles are there?
Name as many triangles as you can.
What do you notice about these triangles?
Big Idea:
August 27th,28th
Objective: Students will understand how to use similarity to solve triangles
August 28th,29th
Objective: Students will understand how to use similarity to solve problems involving triangles
Students will understand how to find the length of the sides of 30-60-90 and 45-45-90 triangles
30-60-90 Triangles
Solution
Solution
45-45-90 Triangle
August/September
September 2nd, 3rd
Objective: Students will understand how to use similarity to solve problems involving triangles
Students will understand how to use sine and cosine to solve problems involving triangles
September 4th
Objective: Students will understand how to use similarity to solve problems involving triangles
Students will understand how to use sine and cosine to solve problems involving triangles
Students will understand how to use tangent to solve problems involving triangles
Big Idea
September 8th
Objective: Students will understand the definition for the six trigonometric functions
Given a right triangle, students will be able to evaluate the six trigonometric functions

September 9th
Objective: Students will understand how to use inverse trig functions to determine angles in a right triangle
Trigonometric Definitions

Big Idea
September 10th
Objective: Practice solving angle of elevation and angle of depression problems
Solution
September 11th
Objective: Use trigonometry to solve a problem
Understand how to solve triangles that are not right triangles (Law of Sines)
Proof of Law of Sines
Big Idea
September 15th
Objective: Students will understand how to use the Law of Sines to solve triangles

September 16th
Objective: Students will understand how to use the Law of Cosines to solve triangles
Proof of Law of Cosines
Big Idea
September 17th
Objective: Students will understand how to use the Law of Cosines to solve triangles
September 18th
Objective: Students will apply their knowledge of trigonometry to solve problems involving triangles
September 22nd
Objective: Students will understand how to use trigonometry to find the area of triangles.
Big Idea
Area of a Triangle
September 23rd, 24th
Objective: Students will solve problems involving areas of triangles.
Answer: The area of the shaded region is 16.84 square units; so it will take 33.68 ounces of ink.
Extension: What if the company wants to print a logo twice the size as the one shown above. How much ink will be needed?
September 26th
Objective: Students will understand how to determine the resultant distance an object travels.
Students will understand how to describe the resultant direction an object travels.
Describing Direction
Cameron leaves home and walks 20 meters North and then 15 meters East. Describe the distance and direction of Cameron's resultant movement.
Cameron leaves home and walks 20 meters North and then 15 meters in a direction of 30 degrees North of East. Describe the distance and direction of Cameron's resultant movement.
September/October
September 29th
Objective: Students will understand how to determine the resultant distance and direction an object travels.
September 30th
Objective: Students will be able to determine the length and distance of a resultant path.
Students will understand the concept of a vector.
Definition of a Vector
Definition of a Vector
Big Idea:
In describing the length and direction of a path an object moves, we have been using the concept of a
vector.
October 1st & 2nd
Finding the Components of a Vector
Objective: Students will be able to determine the length and distance of a resultant path.
Students will understand how to determine components of a vector given its length and direction.
Students will understand how to determine the length and direction of a vector given its components.
October 6th, 7th
Objective: Understand how to represent a vector using magnitude and direction OR using components
Students will be able to apply vectors to determine the resultant force acting on an object.
Big Idea
October 8th
Objective: Students will understand how to use components to determine a resultant force.
Students will be able to apply vectors to determine the resultant force acting on an object from a variety of angles.
October 9th
Objective: Students will apply vectors to solve a resultant force from three forces
Big Idea
What are the components for the resultant force?
October 13th, 14th
Objective: Students will apply vectors to solve a resultant force from three forces
Students will apply vectors to solve relative motion problems.
Relative Motion Example
October 16th
Vector Algebra
Objective: Review of vectors (solutions to HW)
Students will solve vector algebra questions
October 20th
Objective: Students will apply vectors to solve a navigation problem
October 22nd
Objective: Given uniform circular motion, students will be able to determine the distance traveled (Arc Length)
Given uniform circular motion, students will be able to determine an object's location on a circle
Arc Length
Big Idea
October 23rd
Objective: Given uniform circular motion, students will be able to determine the distance traveled (Arc Length)
Given uniform circular motion, students will be able to determine an object's location on a circle
October 24th, 27th
Big Idea
(New) Definition of Sine & Cosine
Objective: Students will understand how angles are points are related on a (unit) circle
Apply knowledge of circles and trigonometry to solve a problem
October 28th
Objective: Students will understand the relationship between radian angle measure and degrees
Big Idea
October 29th, 30th
Objective: Students will understand the relationship between radian angle measure, degree angle measure, arc length and points on a circle

To access videos:
https://www.educreations.com/
Course Code: VBDWJTK
October 31st
Objective: Students will understand measures of angles that will give same values for sine and cosine
November 5th
Objective: Students will understand measures of angles (in degrees) that will give same values for sine and cosine
(i.e., Students will understand how to use the unit circle to understand symmetry of sine and cosine)
November 6th
Objective: Review for Quiz
November 10th, 11th
Big Idea
Objective: Students will understand how to determine values for six trigonometric functions given any angle
November 12th
Objective: Solve questions involving the six trigonometric functions
November 13th
Objective: Students will understand the special (sixteen) points (in degrees) on a unit circle
Students will understand how to find exact values for trigonometric functions
The 16-point Unit Circle
Special Angles (in degrees) in a Unit Circle
Special Angles (in Degrees & Radians) in a Unit Circle
November 14th
Objective: Students will understand the special (sixteen) points (in radians) on a unit circle
Students will understand how to find exact values for trigonometric functions.
November 17th
Objective: Review from Friday
At this point, we should be able to solve the following questions:
Next, (tomorrow), our goal is to understand how to evaluate trigonometric functions for angles greater than 360 degrees or less than 0 degrees.
November 18th
Objective: Students will understand how to evaluate trigonometric functions for angles greater than 360 or less than 0
Angles Greater than 360
Angles Less than 0
November 19th
Objective: Students will apply their knowledge of circular trigonometry to a problem
Water Wheel
November 21st
Objective: (Review from Algebra) Students will understand how to create and interpret a graph of a function
Example: Temperature vs. Time Graph
November 24th, 25th
Objective: Students will understand how to determine the amplitude and period given a graph of a circular function
Definition of Period
Definition of Amplitude
Amplitude & Period
Big Idea
December
December 1st,2nd
Graph of the Sine Function
Big Idea
Graphs of y= a*sin(bx)
December 3rd
Objective: Students will understand how to graph y = sin x
Students will understand how to graph and identify the amplitude and period for y=a*sin(bx)
December 4th
Objective: Given a sine curve, students will understand how to determine an equation [y=a*sin(bx)]
Our goal today is to determine the amplitude and period of a sine function if we are given its equation.
Objective: Students will understand how to graph y = cos x
Students will understand how to graph and identify the amplitude and period for y=a*cos(bx)
Graphs of Sine and Cosine
December 5th
Objective: Students will understand how to translate (vertical & horizontal shifts) sine and cosine functions
Big Idea: Horizontal Translations
December 8th
Big Idea: Vertical Translations
Objective: Students will understand how to translate (vertical & horizontal shifts) sine and cosine functions
December 9th
Objective: Students will understand the parameters in a sinusoid: y=Asin(B(x-C)) + D or y=Acos(B(x-C))+D
Students will determine a sinusoid given a graph
Example:
Review from Algebra:
Understanding f(x-h) and f(x+h)
December 10th
Objective: Practice finding equation of graphs in the form: y=Asin(B(x-C)) + D or y=Acos(B(x-C))+D

December 12th
Objective: Students will understand features (i.e. x-intercepts, asymptotes, period) for the graph of y = tan x
Recall (a problem from November 19th):
Graph of tangent
Big Idea:
December 15th
December 16th
December 17th
December 18th
Objective: (With Substitute) Students will solve problems from Unit 1: Triangle Trigonometry
Objective: (With Substitute) Students will solve problems from Unit 2: Geometric Vectors
Objective: (With Substitute) Students will solve problems from Unit 3: Circular Functions
Visually Determining Vertical Asymptotes
Objective: Students will review the graph of y = tan x
Students will understand how to determine when a function is zero and when it vertical asymptote(s)
Big Idea
The Graph of y = tan x
December 19th
Graph of y = csc x
Objective: Students will understand how to graph y = sec x and y = csc x
Big Idea
January 5th,7th
Objective: Students will understand how to graph sine and cosine functions in degree and radian mode
January 8th
Objective: Students will understand how to graph y = tan x, y = cot x, y = sec x, and y = csc x
Graphs of y = csc x, y = sec x, y = tan x, y = cot x
January 9th
Objective: Students will understand how to graph y = Atan Bx, y = Acot Bx, y = Asec Bx, and y = Acsc Bx
Objective: Students will understand the parameters in a sinusoid (both degree and radian mode): y=Asin(B(x-C)) + D or y=Acos(B(x-C))+D
Students will determine a sinusoid given a graph
January 13th
January 12th
Objective: Students will understand how to graph y = Atan Bx, y = Acot Bx, y = Asec Bx, and y = Acsc Bx
January 20th
Objective: Midterm Review
January 28th
Negative Angle Measure
Big Idea
Objective: Students will understand the meaning of a negative angle.
Students will understand how to find multiple solutions to sin x = y
Algebra Review: Graphing Inverse Relations
January 29th
Objective: Students will understand the meaning of a negative angle.
Students will understand how to find multiple solutions to sin x = y
Students will understand how to graph an inverse relation for a function
Big Idea
2
3
January 30th
Objective: Students will understand the graph of the inverse of y = sin x
Big Idea
February 2nd
Objective: Understand the inverse of y= sin(x)
Understand the function y = sin^-1(x)
February 3rd
Objective: Find exact value of expressions involving the inverse sine function
February 4th
Objective: Understand the function y = cos^-1(x)
Find exact values involving the inverse cosine function
February 9th
Objective: Review & practice tasks involving inverse sine and cosine.
Big Idea
February 12th
Objective: (Review) Students will understand how to graph y = tanx
(Review) Students will understand how to use the unit circle to evaluate the tangent of special angles.

February 13th
Objective: Understand the inverse of y= tan(x)
Understand the function y = tan^-1(x)
February 18th, 19th
Objective: Understand how to evaluate composite trigonometric and inverse trigonometric functions
Example:
Our goal today is to evaluate composite trigonometric and inverse trigonometric functions for any location on the unit circle:
February 20th

February 23rd
February 24th
February 25th
March 3rd
Objective: Apply trigonometry to solve problems
Objective: Apply trigonometry to solve problems
Objective: Apply trigonometry to solve problems
Objective: Review for quiz
Objective: Use a problem context to derive a trigonometric equation
Devise a strategy for solving a trigonometric equation
March 4th
Objective: Find solutions for trigonometric equations (either algebraically or graphically)
Solving Trigonometric Equations by Graphing
March 9th
Objective: Solve trigonometric equations using by graphing
March 10th
Objective: Solve trigonometric equations analytically
For Example:
March 11th
Objective: Solve trigonometric equations (with multiple angles) analytically
March 12th
Objective: Understand how to analytically solve trigonometric equations with multiple angles
Understand the connection between solving trigonometric equations with a graph and analytically
March 13th, 16th
Objective: Apply knowledge of trigonometry to solve a problem
March 17th
Objective: Solve trigonometric equations using by graphing
Introduce trigonometric identities
March 19th
What is an identity?
Objective: (Review from Algebra) Solving algebraic equations
Students will understand how to determine whether an equation is an identity
March 25th, 26th
Objective: Understand the pythagorean identity sin^2(x)+cos^2(x)=1
Apply knowledge of trigonometry to determine identities
Pythagorean Identity
Example:
April 7th
Objective: Identify and justify trigonometric identities
April 8th
Objective: Solve a problem leading to understanding sin(A+B) and cos(A+B) trigonometric identities
April 9th
Big Idea
sin(A+B) and cos(A+B)
Objective: Understand sin(A+B) and cos(A+B) trigonometric identities
April 10th
Objective: Apply the addition identities for sine and cosine
April 13th,14th
Objective: Understand sin(A-B) and cos(A-B) trigonometric identities
April 17th
Objective: Solve problems involving sin(A+B) and cos(A+B) trigonometric identities
April 15th
Objective: Question/Review on Trigonometric Identities
April 20th
Polar Coordinates
Big Idea: Polar Representations of Point
Objective: Understand polar coordinates (r, theta), specifically, the case with negative r
April 21st
Introduction to Polar Graphs
Objective: Understand how to graph polar equations (without a calculator)
Polar Graphs on the TI-84
April 22nd
Objective: Understand how to graph polar equations without a calculator
April 23rd
Objective: Understand how to graph polar equations with a calculator
Interpret the polar graphs and understand the symbolic and graphical representations of polar graphs
April 24th
Objective: Understand how to graph polar equations with a calculator
Interpret the polar graphs and understand the symbolic and graphical representations of polar graphs
April 27th
Objective: Understand how to graph polar equations with a calculator
Interpret the polar graphs and understand the symbolic and graphical representations of polar graphs
April 29th
Objective: Understand how to convert between rectangular and polar equations
Big Idea
April 30th
Objective: Understand how to convert between rectangular and polar equations
May
May 4th
Objective: (Algebra skills review) Solving literal equations
May 5th,6th
Objective: Understand how to convert between polar and rectangular equations
May 7th
Objective: Understand how to graph and find points on implicitly defined curves
Understand the rectangular and polar representation of a circle
May 8th
Objective: Understand how to find an equation of a circle given its center and radius
May 11th
Finding the center and radius of a circle
Big Idea
Objective: Understand how to find an equation of a circle given its center and radius
May 12th
Objective: Solve problems involving circles and their equations
May 13th
Objective: Understand how to complete the square to identify the center and radius of a circle
May 14th
Objective: Final Exam Review
May 15th
Objective: Final Exam Review
May 18th
Objective: Final Exam Review
Using TI App to Graph Circles
May 20th
Objective: Understand graphs and equations of circles
Use TI Calculator App to graph circles
May 21st
Objective: Understand how to graph an ellipse given its equation
Understand how to find an equation of an ellipse given its graph
Introduction to Ellipse
Big Idea:
May 26th
Objective: Understand how to graph and find an equation for an ellipse
Understand geometric features of an ellipse
Geometry of an Ellipse
May 27th
Calculating the Foci of an Ellipse
Big Idea:
Objective: Understand the geometrical and algebraic properties of ellipses
May 28th
Objective: Understand how to find geometric properties (i.e. foci & axes length) given an equation of an ellipse
Understand how to find an equation of an ellipse given it geometric properties
May 29th
Objective: Solve an ellipse problem
June
June 1st
Objective: Solve an ellipse problem

June 3rd,4th
Objective: Understand ax^2+by^2=c (for negative a or b; i.e., introduce hyperbolas)
Understand why ax^2+by^2=c are called conic sections
Introduction to Hyperbolas
Conic Sections
Conic Sections
June 4th, 5th
Objective: Understand how to sketch a graph of a hyperbola given an equation

http://demonstrations.wolfram.com/ConicSectionsTheDoubleCone/
Imaginary Unit
June 8th, 9th
Objective: Understand how to sketch a graph of a hyperbola given an equation
Understand how to find an equation of a hyperbola given its graph

June 10th
Complex Numbers & DeMoivre's Theorem
June 11th
Objective: Review imaginary and Complex Numbers
Recognize patterns in (a+bi)^n when written in polar form (De Moivre's Theorem)
Objective: Apply DeMoivre's Thm to evaluate (a+bi)^n
SY 2014/2015
September 28th
Objective: Understand how to apply Trigonometry to find areas of triangles.
Big Idea
Area of a Triangle
September 29th, 30th
Objective: Solve a problem involving Areas of Triangles
Big Idea
Big Idea
Big Idea
Inverse Tangent Function
November
January
February
March
April
Completing the square to find the radius and center
Full transcript