Objective: Students will understand how to use similarity criteria to solve problems in geometric figures

What questions could be asked?

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

Answers:

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

Radians and Degrees

Definition of Radian

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

Answers

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