EngageNY
Secant and the Co-Functions
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.
Illustrative Mathematics
The Lighthouse Problem
Long considered the symbol of safe harbor and steadfast waiting, the lighthouse gets a mathematical treatment. The straightforward question of distance to the horizon is carefully presented, followed by a look into the different...
EngageNY
Graphing the Sine and Cosine Functions
Doing is more effective than watching. Learners use spaghetti to discover the relationship between the unit circle and the graph of the sine and cosine functions. As they measure lengths on the unit circle and transfer them to a...
Mathematics Assessment Project
Inscribing and Circumscribing Right Triangles
High schoolers attempt an assessment task requiring them to find the radii of inscribed and circumscribed circles of a right triangle with given dimensions. They then evaluate provided sample responses to consider how to improve their...
Curated OER
Right Triangles and The Unit Circle
Young scholars solve right triangles using trigonometry. In this geometry instructional activity, students use the unit circle to identify different trig values. They identify the six trigonometric identities.
Illustrative Mathematics
Coins in a Circular Pattern
What starts as a basic question of division and remainders quickly turns abstract in this question of related ratios and radii. The class works to surround a central coin with coins of the same and different values, then develops a...
Curated OER
Angles in Standard Positions
Students identify positive and negative angles using the Unit Circle. In this pre-calculus instructional activity, students identify the different angles on a unit circle using the coordinate plane and the four different quadrants as a...
Curated OER
Trigonometric Table
In this trigonometry worksheet, 11th graders convert between degrees and radians using a conversion chart. They use the unit circle to help visualize the relationship between radians and degrees. There is an answer key.
Curated OER
Quadrantal Angles
In this quadrantal angle worksheet, students determine the six trigonometric for each quadrant angle. This one-page worksheet contains 36 problems, with answers printed at the bottom of the page.
University of Adeaide
Basic Trigonometry and Radians
A fabulous set of examples and problems that introduce basic trigonometry concepts, this packet is set apart by the care it takes to integrate both radians and degrees into the material. After defining radians, the author demonstrates...
Curated OER
Trigonometric Ratios
Learners investigate properties of the unit circle using sine, cosine and tangent. They analyze the answers to questions about the unit circle based on a right triangle.
Curated OER
Trigonometric Functions of Special Angles
Students explore the concept of the six trigonometric functions, places where the functions can be utilized, and apply these functions to several electrical application problems.
Rice University
Precalculus
Take a step beyond Algebra 2. Learners use the eBook to learn concepts from the typical Precalculus course. Content starts off with a short review of functions in general and moves on to the basic functions, finishing up with more...
Rice University
Algebra and Trigonometry
Move on into trigonometry. An informative eBook takes the content of a College Algebra course and adds more relating to trigonometry and trigonometric functions. The content organization allows pupils to build upon their learning by...
Concord Consortium
Line of Sight
There's no way around it—learners must use trigonometry to model the line of sight around a race track! Using the starting line as the origin, pupils model the straight line distance to any car using a trigonometric expression. The...
Curated OER
Circles
In this circles activity, 10th graders solve and complete 20 different problems related to various circles. First, they find the radius and diameter of a circle with a given circumference. Then, students determine the measure of each...
101 Questions
Ferris Wheel
Around and around you'll go! Learners analyze the periodic nature of a Ferris wheel. Using a trigonometric function, they make predictions about the location of a specific car at the end of the ride and its total trips around the circle.
Illustrative Mathematics
Satellite
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 stations....
Curated OER
Unit Circle & Trig Functions
In this trig functions worksheet, learners determine the exact value of given trigonometric functions. They label degrees, radians and coordinates of given points on a circle. This two-page worksheet contains approximately 20 multi-step...
Curated OER
The Unit Circle
High schoolers relate the trigonometric functions to the coordinates of the unit circle. They classify trigonometric functions as odd or even. Students determine the signs of trigonometric functions in each quadrant. They are...
Curated OER
Woody Sine
Students explore the concept of sine. For this sine lesson, students create a sine graph from tooth picks. Students create a unit circle with tooth pick length radius. Students then take the tooth picks from the unit circle and put them...
EngageNY
Tangent Lines and the Tangent Function
Construct tangent lines and make the connection to tangent functions. An informative instructional activity reviews the geometry origins of the tangent function. Pupils use that information to determine how to construct a tangent to a...
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,...
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...