EngageNY
Why Call It Tangent?
Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of the...
EngageNY
Graphing the Tangent Function
Help learners discover the unique characteristics of the tangent function. Working in teams, pupils create tables of values for different intervals of the tangent function. Through teamwork, they discover the periodicity, frequency, and...
Curated OER
Worksheet 7: Slope and Tangents
Providing both review and practice problems, this worksheet prompts students to answer five questions having to do with slope, tangents lines, graphing, the Squeeze Theorem, differentiable functions and derivatives. This activity could...
CK-12 Foundation
Tangent Line Approximation: Estimating Square Roots
Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...
EngageNY
Tangent Lines and the Tangent Function
Construct tangent lines and make the connection to tangent functions. An informative lesson reviews the geometry origins of the tangent function. Pupils use that information to determine how to construct a tangent to a circle from a...
EngageNY
Tangent Segments
What's so special about tangents? Learners first explore how if a circle is tangent to both rays of an angle, then its center is on the angle bisector. They then complete a set of exercises designed to explore further properties and...
EngageNY
Properties of Tangents
You know about the tangent function, but what are tangent lines to a circle? Learners investigate properties of tangents through constructions. They determine that tangents are perpendicular to the radius at the point of tangency, and...
EngageNY
Applying Tangents
What does geometry have to do with depression? It's an angle of course! Learners apply the tangent ratio to problem solving questions by finding missing lengths. Problems include angles of elevation and angles of depression. Pupils make...
EngageNY
Equations for Tangent Lines to Circles
Don't go off on a tangent while writing equations of tangent lines! Scholars determine the equations for tangent lines to circles. They attempt both concrete and abstract examples, such as a tangent line to the unit circle through (p, 0).
EngageNY
The Inscribed Angle Alternate – A Tangent Angle
You know the Inscribed Angle Theorem and you know about tangent lines; now let's consider them together! Learners first explore angle measures when one of the rays of the angle is a tangent to a circle. They then apply their newfound...
CK-12 Foundation
Slope of a Tangent Line: Slope of the Tangent and Secant Lines
Learn to find the slope through a single point. The interactive provides a visualization of how to find the slope of a tangent line. With the aid of the visualization, pupils see the definition of the derivative in action. Class members...
Curated OER
Tangent Lines and the Radius of a Circle
Your Geometry learners will collaboratively prove that the tangent line of a circle is perpendicular to the radius of the circle. A deliberately sparse introduction allows for a variety of approaches to find a solution.
Illustrative Mathematics
Tangent to a Circle From a Point
Learners see application of construction techniques in a short but sophisticated problem. Combining the properties of inscribed triangles with tangent lines and radii makes a nice bridge between units, a way of using information about...
EngageNY
Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams
First angle measures, now segment lengths. High schoolers first measure segments formed by secants that intersect interior to a circle, secants that intersect exterior to a circle, and a secant and a tangent that intersect exterior to a...
CK-12 Foundation
Horizontal Translations or Phase Shifts: Tangent
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...
Flipped Math
Tangents to Circles
Touch a circle once. Individuals watch a video and learn two theorems related to tangents and circles. The pupils then apply the theorems to find missing angle measures and lengths in figures. At the end, they practice their skills on...
Shodor Education Foundation
Derivate
Derive tangent lines through derivatives. Scholars use an app to graph functions and investigate derivatives and tangent lines. The interactive automatically graphs a tangent line at a specified point and can also produce tables of values.
Curated OER
The Tangent Ratio
Students calculate the tangent ratio given a right triangle. For this trigonometry lesson, students use a right triangle and the Pythagorean Theorem to solve problems.
Texas Instruments
Exploring Tangents
Explore the concept of tangent lines. In this tangent line lesson, learners graph a circle and two lines on their graphing calculator using Cabri Jr. Students construct the lines so that they both intersect at a given point and are both...
Curated OER
Tangents, Secants, and Chords
In this tangents, secants and chords worksheet, 10th graders identify and solve 48 different problems that include using 3 different theorems for defining circles. First, they determine the area of each circle with C as the center and a...
Curated OER
Tangent Lines
In this tangent lines worksheet, 10th graders solve and complete 13 various types of problems. First, they solve the right triangles for the variables shown. Then, students name a radius, a diameter, a tangent, a secant, a point of...
Curated OER
Tangents
In this tangents worksheet, high schoolers determine the length of a missing side of a right triangles. They use tangent lines to solve problems. This two-page worksheet contains 11 multi-step problems.
Curated OER
Segments Formed by Intersectiong Chords, Secants, and Tangents
Learners investigate the properties of segments formed which chords, secants, and tangents, intersect. The dynamic nature of Cabri Jr. allows students to form and verify conjectures regarding segment relationships.
Curated OER
Tangents Multiple Choice
For this circles worksheet, students solve 10 multiple choice problems. Students use a diagram of a circle with tangent lines and segment bisectors to answer each question. Students find unknown segment lengths using the given information.
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