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Unit: Trigonometry

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Possible mastery points

Law of sines

Learn
Solving for a side with the law of sines
(Opens a modal)
Solving for an angle with the law of sines
(Opens a modal)
Proof of the law of sines
(Opens a modal)
Practice
Solve triangles using the law of sinesGet 3 of 4 questions to level up!

Law of cosines

Learn
Solving for a side with the law of cosines
(Opens a modal)
Solving for an angle with the law of cosines
(Opens a modal)
Proof of the law of cosines
(Opens a modal)
Practice
Solve triangles using the law of cosinesGet 3 of 4 questions to level up!

Solving general triangles

Learn
Trig word problem: stars
(Opens a modal)
Laws of sines and cosines review
(Opens a modal)
Practice
General triangle word problemsGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 300 Mastery points

Unit circle introduction

Learn
Unit circle
(Opens a modal)
The trig functions & right triangle trig ratios
(Opens a modal)
Trig unit circle review
(Opens a modal)
Practice
Unit circleGet 3 of 4 questions to level up!

Radians

Learn
Intro to radians
(Opens a modal)
Radians & degrees
(Opens a modal)
Degrees to radians
(Opens a modal)
Radians to degrees
(Opens a modal)
Radian angles & quadrants
(Opens a modal)
Practice
Radians & degreesGet 3 of 4 questions to level up!
Unit circle (with radians)Get 3 of 4 questions to level up!

The Pythagorean identity

Learn
Proof of the Pythagorean trig identity
(Opens a modal)
Using the Pythagorean trig identity
(Opens a modal)
Pythagorean identity review
(Opens a modal)
Practice
Use the Pythagorean identityGet 3 of 4 questions to level up!

Trigonometric values of special angles

Learn
Trig values of π/4
(Opens a modal)
Practice
Trig values of special anglesGet 3 of 4 questions to level up!

Quiz 2

Level up on the above skills and collect up to 500 Mastery points

Graphs of sin(x), cos(x), and tan(x)

Learn
Graph of y=sin(x)
(Opens a modal)
Intersection points of y=sin(x) and y=cos(x)
(Opens a modal)
Graph of y=tan(x)
(Opens a modal)

Amplitude, midline, & period

Learn
Features of sinusoidal functions
(Opens a modal)
Midline, amplitude, and period review
(Opens a modal)
Practice
Midline of sinusoidal functions from graphGet 3 of 4 questions to level up!
Amplitude of sinusoidal functions from graphGet 3 of 4 questions to level up!
Period of sinusoidal functions from graphGet 3 of 4 questions to level up!

Transforming sinusoidal graphs

Learn
Amplitude & period of sinusoidal functions from equation
(Opens a modal)
Transforming sinusoidal graphs: vertical stretch & horizontal reflection
(Opens a modal)
Transforming sinusoidal graphs: vertical & horizontal stretches
(Opens a modal)
Practice
Amplitude of sinusoidal functions from equationGet 3 of 4 questions to level up!
Midline of sinusoidal functions from equationGet 3 of 4 questions to level up!
Period of sinusoidal functions from equationGet 3 of 4 questions to level up!

Quiz 3

Level up on the above skills and collect up to 600 Mastery points

Graphing sinusoidal functions

Learn
Example: Graphing y=3⋅sin(½⋅x)-2
(Opens a modal)
Example: Graphing y=-cos(π⋅x)+1.5
(Opens a modal)
Sinusoidal function from graph
(Opens a modal)
Practice
Graph sinusoidal functionsGet 3 of 4 questions to level up!
Construct sinusoidal functionsGet 3 of 4 questions to level up!
Graph sinusoidal functions: phase shiftGet 3 of 4 questions to level up!

Sinusoidal models

Learn
Interpreting trigonometric graphs in context
(Opens a modal)
Trig word problem: modeling daily temperature
(Opens a modal)
Trig word problem: modeling annual temperature
(Opens a modal)
Trig word problem: length of day (phase shift)
(Opens a modal)
Practice
Interpreting trigonometric graphs in contextGet 3 of 4 questions to level up!
Modeling with sinusoidal functionsGet 3 of 4 questions to level up!
Modeling with sinusoidal functions: phase shiftGet 3 of 4 questions to level up!

Quiz 4

Level up on the above skills and collect up to 600 Mastery points
Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 2000 Mastery points!

About this unit

In Mathematics II, students learned about the trigonometric ratios sine, cosine, and tangent. In this unit, we extend these ideas into functions that are defined for all real numbers! We learn about the behavior of those functions and use them to model real-world situations.