Solve mathematical and real-world problems involving one-variable trigonometric ratios.
| Name |
Description |
| Deriving and Applying the Law of Sines | Students will be introduced to a derivation of the Law of Sines and apply the Law of Sines to solve triangles. |
| The Seven Circles Water Fountain | Students will apply concepts related to circles, angles, area, and circumference to a design situation. |
| Sine and Cosine Relationship between Complementary Angles | This is a lesson on the relationship between the Sine and Cosine values of Complementary Angles. |
| Discovering Trigonometric Ratios | Students investigate and discover trigonometric ratios by drawing and measuring side lengths for five triangles that have equivalent angle measure. Students collect, analyze, and discuss data to draw conclusions. This is the introductory lesson to facilitate student discovery of trigonometric ratios and allows students to secure a solid foundation before the use of trigonometry to find missing sides. This lesson has students solving application problems by finding an unknown angle based on length measurements. |
| The Copernicus' Travel | This lesson uses Inverse Trigonometric Ratios to find acute angle measures in right triangles. Students will analyze the given information and determine the best method to use when solving right triangles. The choices reviewed are Trigonometric Ratios, The Pythagorean Theorem, and Special Right Triangles. |
| The Trig Song | This lesson is a group project activity designed to reinforce the concepts of sine and cosine. The lesson begins with a spiral review of the concepts, which will move into the group project - writing an original song to demonstrate understanding and application of sine and cosine ratios. |
| How Tall am I? | Students will determine the height of tall objects using three different calculation methods. They will work in groups to gather their data and perform calculations. A whole-class discussion is conducted at the end to compare results and discuss some of the possible errors. |
| Are You Pulling My Trig? | This lesson is an introduction of the application of trigonometric ratios. Students will solve real-world word problems using trigonometric ratios of sine, cosine and tangent. |
| Let's Get "Triggy" | This lesson helps students discover trigonometric ratios and how to apply them to find the measure of sides and angles of a right triangle. Students will think about problems, discuss concepts with a partner and then share ideas with the class. Students will collaborate and offer supportive coaching to help deepen each other’s understanding. |
| Survey Says... We're Using TRIG! | This lesson is meant as a review after being taught basic trigonometric functions. It will allow students to see and solve problems from a real-world setting. The Perspectives video presents math being used in the real-world as a multimedia enhancement to this lesson. Students will find this review lesson interesting and fun. |
| Name |
Description |
| Coins in a circular pattern | Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin. (For this task, United States coins are used, but the task can be adapted for coins from other countries.) |
| Finding the area of an equilateral triangle | This problem solving task asks students to find the area of an equilateral triangle. Various solutions are presented that include the Pythagoren theorem and trigonometric functions. |
| The Lighthouse Problem | This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat. |
| Seven Circles III | This provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function. |
| Setting Up Sprinklers | This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles, using trigonometric ratios to solve right triangles, and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found. |
| Name |
Description |
| Coins in a circular pattern: | Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin. (For this task, United States coins are used, but the task can be adapted for coins from other countries.) |
| Finding the area of an equilateral triangle: | This problem solving task asks students to find the area of an equilateral triangle. Various solutions are presented that include the Pythagoren theorem and trigonometric functions. |
| The Lighthouse Problem: | This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat. |
| Setting Up Sprinklers: | This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles, using trigonometric ratios to solve right triangles, and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found. |
| Name |
Description |
| Coins in a circular pattern: | Using a chart of diameters of different denominations of coins, students are asked to figure out how many coins fit around a central coin. (For this task, United States coins are used, but the task can be adapted for coins from other countries.) |
| Finding the area of an equilateral triangle: | This problem solving task asks students to find the area of an equilateral triangle. Various solutions are presented that include the Pythagoren theorem and trigonometric functions. |
| The Lighthouse Problem: | This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat. |
| Setting Up Sprinklers: | This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles, using trigonometric ratios to solve right triangles, and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found. |
