Schoolcraft College
Trigonometry
This trigonometry textbook takes the learner from a basic understanding of angles and triangles through the use of polar coordinates on the complex plane. Written by a mathematician-engineer, examples and problems here are used to...
Teach Engineering
Solar Angles and Tracking Systems
The sun will continue to rise in the east and set in the west, no matter what. The first lesson plan 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...
Flipped Math
Intro to Trigonometry
Expand trigonometric ratios beyond right triangles. Pupils start with a review of trigonometric ratios and then take a look at angles in standard position to determine their measurements. Scholars discover how to find coterminal angles...
CK-12 Foundation
Double Angle Identities: Ferris Wheel
Use a Ferris wheel to soar to new heights of understanding on double angle identities. Here is an interactive that applies an example of a Ferris wheel to show how doubling the angle does not double the value of a trigonometric ratio....
Mathed Up!
Trigonometry
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.
CK-12 Foundation
Angle-Angle-Side Triangles: Garden Gate
Good fences make good gardens. Individuals use an interactive to see how angles and sides relate in a triangular-shaped garden fence. They apply the Law of Sines to find the length of the garden gate (third side of triangle) given two...
CK-12 Foundation
Law of Cosines: Angles in the Outfield
Take me out to the trig class. Individuals use an interactive to see how angles on a baseball field change as the position of two runners change. A set of challenge questions has them apply the Law of Cosines to solve problems.
CK-12 Foundation
Possible Triangles with Side-Side-Angle
It's not often that math allows for multiple answers. Young mathematicians identify possible numbers of triangles when given two sides and a non-included angle. An interactive helps with this investigation.
CK-12 Foundation
Angles of Elevation and Depression: Fly-By Calibration
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.
EngageNY
Special Triangles and the Unit Circle
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...
CK-12 Foundation
Angle-Side-Angle Triangles: Caution Tape
Don't lose your marbles. Scholars use an interactive to create a triangle that closes off a portion of a sidewalk with loose marbles. The Law of Sines helps them find the side measures of such a triangle.
CK-12 Foundation
Unit Circle: Medieval Castle Defense
Who needs a plan — let trigonometry protect you! Pupils determine the angle of an approaching enemy to a village wall. The scholars determine the exact value of trigonometric functions for the angle. Class members use trigonometry to...
CK-12 Foundation
Pythagorean Theorem for Solving Right Triangles: Solving the Triangle
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...
Flipped Math
Trig Ratios
Take ratios of sides to a new level. Pupils learn the definitions of the three basic trigonometric ratios in right triangles. Using the definitions, scholars find missing lengths in right triangles, based on a known angle. Individuals...
EngageNY
An Area Formula for Triangles
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....
EngageNY
Inverse Trigonometric Functions
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...
EngageNY
Addition and Subtraction Formulas 2
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,...
Flipped Math
Inverse Trig Ratios
Put trigonometric ratios into inverse. Scholars learn how to find an unknown angle in a right triangle by using inverse trigonometric ratios. The pupils understand how the inverses undo a trigonometric ratio to provide the angle measure....
CK-12 Foundation
Basic Trigonometric Functions: Ladder Length
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...
Radford University
Trouble in the Orchard
It's no fun catching a fungus. Scholars first investigate how the seasons affect the angle of the sun and the lengths of shadows. They then apply right triangle trigonometry to determine the height of trees based on their shadows to...
EngageNY
Addition and Subtraction Formulas 1
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...
CK-12 Foundation
Sine, Cosine, and Tangent Functions: Lighthouse
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...
CK-12 Foundation
Secant, Cosecant, and Cotangent Functions: Hold the Ladder!
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...
CK-12 Foundation
Law of Cosines: Get on Base
Baseball is all about math. Young baseball and mathematics enthusiasts determine the distance between players on a baseball field using the Law of Cosines. An interactive helps them find relevant distances and angles to use in their...