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Interactive
CK-12 Foundation

Basic Trigonometric Functions: Ladder Length

For Students 9th - 12th Standards
Climb the ladder to trigonometry. The interactive introduces trigonometric ratios and finding lengths of sides of right triangles created by a ladder and a building. Learners use the interactive to create triangles by moving the top of...
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Lesson Plan
Virginia Department of Education

Special Right Triangles and Right Triangle Trigonometry

For Teachers 9th - 11th Standards
Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...
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Assessment
Mathed Up!

Trigonometry

For Students 10th - 12th
Learn how to solve a triangle. Young mathematicians view a video that explains how to apply trigonometry to find missing sides and angles of a right triangle. A worksheet tests their understanding of the concept.
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Assessment
Illustrative Mathematics

Hours of Daylight 1

For Students 9th - 12th Standards
The midline of the mathematical model of the number of hours of sunlight is not 12 hours. Pupils use the modeling cycle to determine a function that will model the number of hours of sunlight at a location of their choosing. Using...
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Assessment
Illustrative Mathematics

Foxes and Rabbits 2

For Students 9th - 12th Standards
The fox population chases the rabbit population. Groups model the populations of foxes and rabbits with two trigonometric functions. Individuals graph both trigonometric models on the same graph, and then teams determine an explanation...
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Assessment
Illustrative Mathematics

As the Wheel Turns

For Students 9th - 12th Standards
Determine the location of a point on a moving wheel. The task challenges groups to determine the horizontal and vertical locations of a point on the edge of wheel that is moving. Teams first determine a function that will model the...
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Assessment
Illustrative Mathematics

Foxes and Rabbits 3

For Students 9th - 12th Standards
Model periodic populations. Here, in the context of foxes and rabbits, pupils look at graphs of the populations of these animals in a national park over a span of 24 months. Groups analyze the graphs and determine trigonometric functions...
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Assessment
EngageNY

End-of-Module Assessment Task: Pre-Calculus Module 4

For Students 11th - 12th Standards
Challenge your scholars to show what they know about the Law of Sines, Law of Cosines, and inverses. The six-question assessment is the last in a series of 16. Pupils find the area of triangles and show that the Law of Sines and Law of...
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Lesson Plan
EngageNY

Inverse Trigonometric Functions

For Teachers 11th - 12th Standards
Build on the understanding of finding angles using trigonometric ratios. Pupils develop the definitions of inverse trigonometric functions by restricting their domains in the 13th lesson of a 16-part series. They use inverse functional...
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Lesson Plan
EngageNY

Putting the Law of Cosines and the Law of Sines to Use

For Teachers 11th - 12th Standards
Use the Law of Cosines and the Law of Sines to solve problems using the sums of vectors. Pupils work on several different types of real-world problems that can be modeled using triangles with three known measurements. In the process,...
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Lesson Plan
EngageNY

Law of Cosines

For Teachers 11th - 12th Standards
Build upon the Pythagorean Theorem with the Law of Cosines. The 10th part of a 16-part series introduces the Law of Cosines. Class members use the the geometric representation of the Pythagorean Theorem to develop a proof of the Law of...
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Lesson Plan
EngageNY

An Area Formula for Triangles

For Teachers 11th - 12th Standards
Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....
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Lesson Plan
EngageNY

Addition and Subtraction Formulas 1

For Teachers 11th - 12th Standards
Show budding mathematicans how to find the sine of pi over 12. The third lesson in a series of 16 introduces the addition and subtraction formulas for trigonometric functions. Class members derive the formulas using the distance formula...
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Lesson Plan
EngageNY

Modeling with Inverse Trigonometric Functions 2

For Teachers 11th - 12th Standards
Use inverse trigonometric functions to work with ramps, rabbits, and Talladega. The class models real-world situations with trigonometric functions and solves them using inverses in the 15th installment of a 16-part series. Pupils solve...
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Lesson Plan
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EngageNY

Revisiting the Graphs of the Trigonometric Functions

For Teachers 11th - 12th Standards
Use the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...
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Lesson Plan
EngageNY

Law of Sines

For Teachers 11th - 12th Standards
Prove the Law of Sines two ways. The ninth segment in a series of 16 introduces the Law of Sines to help the class find lengths of sides in oblique triangles. Pupils develop a proof of the Law of Sines by drawing an altitude and a second...
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Assessment
EngageNY

Mid-Module Assessment Task: Pre-Calculus Module 4

For Students 11th - 12th Standards
Challenge scholars to show what they know about properties and addition and subtraction formulas for trigonometric functions. The resource provides a mid-unit check on the progress toward mastery of trigonometric concepts. The areas...
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Lesson Plan
EngageNY

Addition and Subtraction Formulas 2

For Teachers 11th - 12th Standards
Knowing the addition formulas allows for the calculations of double and half formulas. The fourth installment of 16 has the class use the addition formula to develop the double angle trigonometric formulas. Using the double formula,...
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Lesson Plan
EngageNY

Special Triangles and the Unit Circle

For Teachers 11th - 12th Standards
Calculate exact trigonometric values using the angles of special right triangles. Beginning with a review of the unit circle and trigonometric functions, class members use their knowledge of special right triangles to find the value of...
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Assessment
Inside Mathematics

Hopewell Geometry

For Teachers 9th - 12th Standards
The Hopewell people of the central Ohio Valley used right triangles in the construction of earthworks. Pupils use the Pythagorean Theorem to determine missing dimensions of right triangles used by the Hopewell people. The assessment task...
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Lesson Plan
EngageNY

Trigonometry and Complex Numbers

For Teachers 11th - 12th Standards
Complex numbers were first represented on the complex plane, now they are being represented using sine and cosine. Introduce the class to the polar form of a complex number with the 13th part of a 32-part series that defines the argument...
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Lesson Plan
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Teach Engineering

Solar Angles and Tracking Systems

For Teachers 9th - 12th
The sun will continue to rise in the east and set in the west, no matter what. The first lesson in a series of eight introduces the class to solar angles. It makes connections between a person's latitude and the angle of position of the...
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PPT
Urbana School District

Vectors

For Teachers 11th - Higher Ed Standards
I don't always make vector jokes, but when I do, IJK. Vector addition using multiple methods, scalar multiplication, vector subtraction, vector components, relative velocities, free body diagrams, and so much more Are covered in this...
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PPT
Urbana School District

Projectile and Circular Motion, Torque

For Teachers 11th - Higher Ed Standards
Introduce your young scholars to the concepts of circular motion, projectile motion, angular speed, simple harmonic motion, torque, center of mass, centripetal force, and Hooke's Law with a 86-slide presentation. The circular motion...