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Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Sine

For Students 10th - 12th Standards
Shift a trigonometric function and find its new equation. Pupils translate a sine function on a graph. The scholars determine the equation of the function that represents the translated graph and observe the connection between a...
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Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Tangent

For Students 10th - 12th Standards
Patterns can be shifty! Find the pattern when shifting the graph of tangent. Pupils move the graph of tangent to different locations on the coordinate plane. They observe what happens to the function and its vertical asymptotes before...
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Interactive
CK-12 Foundation

Changes in Period and Amplitude of the Sine Function

For Students 10th - 12th Standards
How does a change in amplitude or period affect the equation of a sine function? Scholars move sliders to change the frequency and period of the sine function. The interactive displays the resulting equation, and pupils determine the...
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Interactive
CK-12 Foundation

Translating Sine and Cosine Functions: Translating Sine

For Students 10th - 12th Standards
Learn how to slide sine back and forth and up and down. Pupils move the starting point of a graph of sine vertically and horizontally. They investigate the changes to the equation of the graph in relationship to the translation. They...
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Interactive
CK-12 Foundation

Trigonometric Functions and Angles of Rotation: The Triangle in the Circle

For Students 10th - 12th Standards
Go around the unit circle and create triangles. Pupils move a point around the unit circles to visualize the triangle associated with the angle in standard position. The three main trigonometric functions are defined in terms of the legs...
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Interactive
CK-12 Foundation

Right Triangles, Bearings, and Other Applications: Sailing Race

For Students 9th - 12th Standards
Help your class get their bearings when it comes to right triangles. Pupils determine distances traveled or components given the bearing of a sailboat using an interactive. The scholars develop a sense of finding the bearings of a given...
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Interactive
CK-12 Foundation

Pythagorean Theorem for Solving Right Triangles: Solving the Triangle

For Students 9th - 12th Standards
Observe the change in the trigonometric ratios as angles vary. An interactive provides the values of trigonometric ratios for both acute angles in a right triangle. Pupils create a right triangle to match given criteria and find the...
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Interactive
CK-12 Foundation

Secant, Cosecant, and Cotangent Functions: Hold the Ladder!

For Students 9th - 12th Standards
Determine the length of a falling ladder. Pupils use an interactive to find the angle a ladder makes with the floor after it falls to answer questions. The scholars use the triangle formed in the interactive to determine values of...
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Interactive
CK-12 Foundation

Sine, Cosine, and Tangent Functions: Lighthouse

For Students 9th - 12th Standards
How far is that boat from the lighthouse? Scholars create diagrams to represent a scenario given the angle of depreciation from a lighthouse to a boat. Learners apply the basic trigonometric functions to find various distances stemming...
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Interactive
CK-12 Foundation

Angles of Elevation and Depression: Fly-By Calibration

For Students 9th - 12th Standards
Determine the distance between two trees from afar. Pupils use an interactive resource to create two right triangles using trees and a plane. They determine the horizontal legs of each triangle to find the distance between the two trees.
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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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Interactive
McGraw Hill

Stellar Parallax Interactive

For Students 9th - Higher Ed
How are scientists able to measure distances between stellar bodies? Turns out it's not very easy! Learners explore the process of trigonometric parallax as the method of determining these distances. They experience the same challenges...
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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

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

Sum and Difference Angle Formulas

For Students 9th - 12th Standards
Need practice deriving trigonometric angle formulas? With this worksheet, pupils derive the sum and difference formulas for cosine and tangent and the difference formula for sine. Scholars use the sine sum formula and other known...
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Lesson Plan
EngageNY

Waves, Sinusoids, and Identities

For Teachers 11th - 12th Standards
What is the net effect when two waves interfere with each other? The lesson plan answers this question by helping the class visualize waves through graphing. Pupils graph individual waves and determine the effect of the interference...
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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

Modeling with Inverse Trigonometric Functions 1

For Teachers 11th - 12th Standards
Where should I stand to get the best view? Pupils use inverse trigonometric functions to determine the horizontal distance from an object to get the best view. They round out the lesson plan by interpreting their answers within context.
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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

Properties of Trigonometric Functions

For Teachers 11th - 12th Standards
Given a value of one trigonometric function, it is easy to determine others. Learners use the periodicity of trigonometric functions to develop properties. After studying the graphs of sine, cosine, and tangent, the lesson connects them...