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...

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...

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...

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...

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...

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,...

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...

Young mathematicians identify different cases of intersecting secant lines. They then investigate the case where secant lines meet inside a circle.

Circles are the foundation of many geometric concepts and extensions - a point that is thoroughly driven home in this extensive unit. Fundamental properties of circles are investigated (including sector area, angle measure, and...

Make the connection between the distance formula and the equation of a circle. The teacher presents a lesson on how to use the distance formula to derive the equation of the circle. Pupils transform circles on the coordinate plane and...

Don't circle around the topic, but get right to the center with tons of practice regarding circles in geometry. The note-incorporated learning exercise provides guided practice through many topics such as central angles, inscribed...

Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...

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...

Here's some very interesting circles for your very interested pupils. A performance task requires scholars to sketch a pair of orthogonal circles so the centers are the endpoints of one side of a triangle. They draw an additional circle...

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...

Learning about tangents doesn't have to be a slippery slope. Pupils drag a point around a unit circle to see how angle affects the slope of a line. They individually answer a set of challenge questions to come to the conclusion that...

It doesn't matter whether secant lines intersect inside or outside the circle, right? Scholars extend concepts from the previous lesson to investigate angles created by secant lines that intersect at a point exterior to the circle....

A steal of a deal — get four angles for the value of one. An interactive resource allows individuals to visualize all four angles that have the same reference angle. Pupils answer questions by using the interactive to create the...

The slope makes a difference. Given an equation of a circle and point, scholars determine the relationship of the slope of a line through the point and the number of intersections with the circle. After graphing the relationship, pupils...

Learners practice relating rules of trigonometry and properties of circles. With a few simplifying assumptions such as a perfectly round earth, young mathematicians calculate the lengths of various paths between satellite and...

Noah didn't construct this kind of arc. High school scholars first explore how angles can be formed in circles. They then learn relationships between angles and arcs by conducting an exploratory activity where they position and draw arcs...

Your learners combine their knowledge of real and imaginary numbers and matrices in an activity containing thirty lessons, two assessments (mid-module and end module), and their corresponding rubrics. Centered on complex numbers and...

Turn your class upside down as they explore the reciprocal functions. Scholars use the unit circle to develop the definition of the secant and cosecant functions. They analyze the domain, range, and end behavior of each function.

Spin through the trigonometric functions. Scholars determine the angle of rotation a snowboarding snowman makes at various distances in his jump. The class members then calculate the values of trigonometric functions for those angles.