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How to prove quotient and reciprocal identities

Grade 11 Math: Master Advanced Concepts & Skills

11F.A1.1

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Introduction to quadratic functions

Domain and range of a function

Identifying functions

Function notation

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

11F.A1.2

Characteristics of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Graphing quadratic functions: General form VS. Vertex form

11F.A1.3

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

11F.A1.4

Inverse functions

11F.A1.5

Finding inverse trigonometric function from its graph

11F.A1.6

One to one functions

11F.A1.8

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

11F.A1.9

Combining transformations of functions

11F.A2.1

Nature of roots of quadratic equations: The discriminant

11F.A2.2

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

11F.A2.3

Applications of quadratic functions

Applications of quadratic equations

11F.A2.4

Transformations of quadratic functions

Finding the quadratic functions for given parabolas

11F.A2.5

System of linear-quadratic equations

11F.A3.1

Factor by taking out the greatest common factor

Factor by taking out GCF

Factoring trinomials

Factoring Trinomials

Multiplying polynomial by polynomial

11F.A3.2

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

11F.A3.3

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

11F.B1.1

Graphing exponential functions

11F.B1.2

Exponents: Rational exponents

11F.B1.3

Convert between radicals and rational exponents

11F.B2.2

Graphing transformations of exponential functions

11F.B2.4

Solving exponential equations using exponent rules

11F.B2.5

Finding an exponential function given its graph

11F.B3.2

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

11F.C1.1

Introduction to sequences

11F.C1.5

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

11F.C1.6

Binomial theorem

11F.C2.1

Arithmetic sequences

Geometric sequences

11F.C2.3

Arithmetic series

Arithmetic series formula

Geometric series

Geometric Series

11F.C3.1

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

11F.C3.2

Finance: Compound interest

Finance: Compound Interest

11F.C3.5

Finance: Future value and present value

11F.D1.1

Find the exact value of trigonometric ratios

11F.D1.3

ASTC rule in trigonometry (<b>A</b>ll <b>S</b>tudents <b>T</b>ake <b>C</b>alculus)

ASTC rule in trigonometry

11F.D1.4

Inverse reciprocal trigonometric function: finding the exact value

Inverse Reciprocal Trigonometric Function: Finding the Exact Value

11F.D1.5

Quotient identities and reciprocal identities

Pythagorean identities

11F.D1.6

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

11F.D2.1

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

11F.D2.5

Graphing transformations of trigonometric functions

11F.D2.8

Determining trigonometric functions given their graphs

11F.D3.2

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

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Grade 11 Functions, University Preparation (MCR3U) 

A. Characteristics of Functions

B. Exponential Functions

C. Discrete Functions

D. Trigonometric Functions

math

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Ex. 1:

Ex. 2:

Don't be scared by all the trigonometric identities formulas in this chapter! Dennis will show you how to easily simplify and prove quotient identities and reciprocal identities.

Use sine ratio to calculate angles and sides (Sin = \(  \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos =  \(  \frac{a}{h}\)  )

Use tangent ratio to calculate angles and sides (Tan =  \(  \frac{o}{a}\)  )