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Transformation of trigonometric functions

Grade 11 Math: Master Advanced Concepts & Skills

11FA.A1.1

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Characteristics of quadratic functions

Applications of quadratic functions

11FA.A1.2

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

Quadratic function in vertex form: y = a(x-p)^2 + q

Multiplying polynomial by polynomial

11FA.A1.3

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

11FA.A1.4

Solving quadratic equations by factoring

11FA.A1.5

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

11FA.A1.6

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

11FA.A1.7

Nature of roots of quadratic equations: The discriminant

11FA.A1.8

Solving quadratic equations by completing the square

Applications of quadratic equations

11FA.A2.1

Identifying functions

Function notation

11FA.A2.2

Function notation (advanced)

11FA.A2.3

Domain and range of a function

11FA.A2.4

Introduction to quadratic functions

11FA.A2.5

Transformations of quadratic functions

11FA.A2.6

Combining transformations of functions

11FA.A2.7

Converting from general to vertex form by completing the square

11FA.A2.8

Completing the square

Completing the Square

11FA.A2.9

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

11FA.B1.1

Exponents: Rational exponents

Convert between radicals and rational exponents

11FA.B1.2

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Combining the exponent rules

11FA.B1.3

Graphing exponential functions

11FA.B1.4

Graphing transformations of exponential functions

11FA.B1.5

Finding an exponential function given its graph

11FA.B2.1

Exponential growth and decay by a factor

11FA.B2.2

Evaluating logarithms using change-of-base formula

Solving exponential equations using exponent rules

11FA.B3.1

Exponential growth and decay by percentage

11FA.B3.2

Exponential decay: Half-life

11FA.B3.3

Finance: Compound interest

Finance: Compound Interest

11FA.C1.1

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

11FA.C1.2

Combination of SohCahToa questions

11FA.C1.3

Law of sines

Ambiguous case: SSA triangles

Law of cosines

11FA.C1.4

Applications of the sine law and cosine law

11FA.C1.5

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

11FA.C2.1

Sine graph: y = sin x

11FA.C2.2

Cosine graph: y = cos x

11FA.C2.3

Tangent graph: y = tan x

11FA.C2.4

Cotangent graph: y = cot x

11FA.C2.5

Secant graph: y = sec x

11FA.C2.6

Cosecant graph: y = csc x

11FA.C2.7

Graphing transformations of trigonometric functions

11FA.C3.1

Determining trigonometric functions given their graphs

11FA.C3.2

Ferris wheel trig problems

11FA.C3.3

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

<p>Aligned with your class and textbook, our comprehensive Grade 11 math help covers all topics that you would expect in any typical grade 11 math classes, whether it&apos;s <a href="http://www.edu.gov.on.ca/eng/curriculum/secondary/grade11.html">Ontario math curriculum</a>, <a href="https://curriculum.gov.bc.ca/curriculum/10-12#m">B.C.</a>, <a href="https://education.alberta.ca/mathematics-10-12/programs-of-study/">Alberta</a>, <a href="http://www.edu.gov.mb.ca/k12/cur/math/framework_9-12/index.html">Manitoba</a>, <a href="https://www.curriculum.gov.sk.ca/webapps/moe-curriculum-BBLEARN/index.jsp?lang=en&subj=mathematics&level=precalc20">Saskatchewan</a>, <a href="http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/">Newfoundland</a>, or other provinces.</p>

<p>Our video lessons walk you through all topics in trigonometry like Unit circle, Factoring trinomials, Radicals, Rational expressions, Quadratic equations, Sequences and series, and so many more. Learn the concepts with our tutorials that show you step-by-step solutions to even the hardest math problems. Then, reinforce your understanding with tons of grade 11 math practice.</p>

<p>All our lessons are taught by experienced Grade 11 Math teachers. Let&apos;s finish your homework in no time, and ACE that final.</p>

Grade 11 Functions and Applications, University/College Preparation (MCF3M)

A. Quadratic Functions

B. Exponential Functions

C. Trigonometric Functions

math

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<p>As a general guideline, before jumping into any of our topics in grade 11 math, we recommend starting with assessing your prior knowledge. This is simply done by reviewing your familiarity with concepts we believe you should have a relatively strong command of. Almost all of our topics begin with an outline on the basic concepts you should know as well as other related, pertinent concepts.</p>
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<p>Last but certainly not the least of these steps, we encourage you to put your knowledge and skills to the test! We&apos;ve prepared plenty of questions per topic for you to master and perfect! See how well you have learnt and acquire more practice from a wide variety and range (i.e. easy to hard) of questions.</p>
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Ex. 1:

Ex. 2:

After learning all the graphs of basic trigonometric functions, in this lesson, we are going to go a little bit further on how the graphs will be transformed as the functions change. The general form for the equation of trig functions is y = <i>f</i> [B(x + c)] + D, where <i>f</i> refers the trig function; A refers to the amplitude/steepness; B represents the period of the graph; C refers to phase shift (left or right) and D represents vertical shift (up or down).  We will learn how to graph the trig function for multiple periods; state the vertical displacement, phase shift, period and amplitude; and also find the domain and range of the transformed functions. 