Trigonometry | 1 Big School (By Blue Brain)

Course Content

Trigonometry with right triangles

Introduction to the trigonometric ratios
Intro to the trigonometric ratios
Trigonometric ratios in right triangles
Solving for a side in a right triangle using the trigonometric ratios
Solving for a side in right triangles with trigonometry
Modeling with right triangles
Right triangle word problem
Trigonometric ratios and similarity
Triangle similarity & the trigonometric ratios
Trig challenge problem: verify identities
Trig challenge problem: trig values & side ratios
Sine and cosine of complementary angles
Sine & cosine of complementary angles
Using complementary angles
Trig word problem: complementary angles
Introduction to the Pythagorean trigonometric identity
Intro to the Pythagorean trig identity
The reciprocal trigonometric ratios
Finding reciprocal trig ratios
Using reciprocal trig ratios

Trigonometry with general triangles

The law of sines
Solving for a side with the law of sines
Solving for an angle with the law of sines
Proof of the law of sines
The law of cosines
Solving for a side with the law of cosines
Solving for an angle with the law of cosines
Proof of the law of cosines
Solving general triangles
Trig word problem: stars
Introduction to radians
Intro to radians
Radians & degrees
Degrees to radians
Radians to degrees
Radian angles & quadrants

The unit circle definition of sine, cosine, and tangent

The unit circle definition of sine, cosine, and tangent
Unit circle
The trig functions & right triangle trig ratios
The graphs of sine, cosine, and tangent
Graph of y=sin(x)
Graph of y=tan(x)
Intersection points of y=sin(x) and y=cos(x)
Basic trigonometric identities
Sine & cosine identities: symmetry
Tangent identities: symmetry
Sine & cosine identities: periodicity
Tangent identities: periodicity
Trigonometric values of special angles
Trig values of special angles
The Pythagorean identity
Proof of the Pythagorean trig identity
Using the Pythagorean trig identity
Long live Tau
Tau versus pi
Pi is (still) wrong
The graphs of sine, cosine, and tangent
Graph of y=sin(x)
Intersection points of y=sin(x) and y=cos(x)
Graph of y=tan(x)
Introduction to amplitude, midline, and extrema of sinusoidal functions
Features of sinusoidal functions

Graphs of trigonometric functions

Finding amplitude and midline of sinusoidal functions from their formulas
Amplitude & period of sinusoidal functions from equation
Period of sinusoidal functions
Amplitude & period of sinusoidal functions from equation
Graphing sinusoidal functions
Transforming sinusoidal graphs: vertical stretch & horizontal reflection
Transforming sinusoidal graphs: vertical & horizontal stretches
Constructing sinusoidal functions
Sinusoidal function from graph
Trig word problem: modeling daily temperature
Trig word problem: length of day (phase shift)
The inverse trigonometric functions
Intro to arcsine
Intro to arctangent
Intro to arccosine
Restricting domains of functions to make them invertible
Domain & range of inverse tangent function
Using inverse trig functions with a calculator
Solving basic sinusoidal equations
Solving sinusoidal equations of the form sin(x)=d
Solving cos(θ)=1 and cos(θ)=-1
Solving sinusoidal models
Trig word problem: solving for temperature

Trigonometric equations and identities

Review of trig angle addition identities
Using the cosine angle addition identity
Using the cosine double-angle identity
Proof of the sine angle addition identity
Proof of the cosine angle addition identity
Introduction to the trigonometric angle addition identities
Finding trig values using angle addition identities
Using trig angle addition identities: finding side lengths
Using trig angle addition identities: manipulating expressions
Using trigonometric identities
Using trigonometric identities to solve problems
Trig challenge problem: area of a hexagon
Trig challenge problem: arithmetic progression
Trig challenge problem: multiple constraints
Trig challenge problem: system of equations
Challenging trigonometry problems

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Course Content

Trigonometry with right triangles

Introduction to the trigonometric ratios

Intro to the trigonometric ratios

Trigonometric ratios in right triangles

Solving for a side in a right triangle using the trigonometric ratios

Solving for a side in right triangles with trigonometry

Modeling with right triangles

Right triangle word problem

Trigonometric ratios and similarity

Triangle similarity & the trigonometric ratios

Trig challenge problem: verify identities

Trig challenge problem: trig values & side ratios

Sine and cosine of complementary angles

Sine & cosine of complementary angles

Using complementary angles

Trig word problem: complementary angles

Introduction to the Pythagorean trigonometric identity

Intro to the Pythagorean trig identity

The reciprocal trigonometric ratios

Finding reciprocal trig ratios

Using reciprocal trig ratios

Trigonometry with general triangles

The law of sines

Solving for a side with the law of sines

Solving for an angle with the law of sines

Proof of the law of sines

The law of cosines

Solving for a side with the law of cosines

Solving for an angle with the law of cosines

Proof of the law of cosines

Solving general triangles

Trig word problem: stars

Introduction to radians

Intro to radians

Radians & degrees

Degrees to radians

Radians to degrees

Radian angles & quadrants

The unit circle definition of sine, cosine, and tangent

The unit circle definition of sine, cosine, and tangent

Unit circle

The trig functions & right triangle trig ratios

The graphs of sine, cosine, and tangent

Graph of y=sin(x)

Graph of y=tan(x)

Intersection points of y=sin(x) and y=cos(x)

Basic trigonometric identities

Sine & cosine identities: symmetry

Tangent identities: symmetry

Sine & cosine identities: periodicity

Tangent identities: periodicity

Trigonometric values of special angles

Trig values of special angles

The Pythagorean identity

Proof of the Pythagorean trig identity

Using the Pythagorean trig identity

Long live Tau

Tau versus pi

Pi is (still) wrong

The graphs of sine, cosine, and tangent

Graph of y=sin(x)

Intersection points of y=sin(x) and y=cos(x)

Graph of y=tan(x)

Introduction to amplitude, midline, and extrema of sinusoidal functions

Features of sinusoidal functions

Graphs of trigonometric functions

Finding amplitude and midline of sinusoidal functions from their formulas

Amplitude & period of sinusoidal functions from equation

Period of sinusoidal functions

Amplitude & period of sinusoidal functions from equation

Graphing sinusoidal functions

Transforming sinusoidal graphs: vertical stretch & horizontal reflection

Transforming sinusoidal graphs: vertical & horizontal stretches

Constructing sinusoidal functions

Sinusoidal function from graph

Trig word problem: modeling daily temperature

Trig word problem: length of day (phase shift)

The inverse trigonometric functions

Intro to arcsine