Exploring Trigonometric Ratios with Calculators

Objective:

Students will be able to calculate trigonometric ratios using a calculator to find missing sides of right triangles.

Assessment:

Students will be assessed through a worksheet where they have to calculate missing sides of right triangles using trigonometric ratios and their calculators.

Key Points:

• Understanding the sine, cosine, and tangent trigonometric ratios.

• Learning how to use a scientific or graphing calculator to calculate trigonometric values.

• Applying trigonometric ratios to find missing sides of a right triangle.

• Recognizing common misconceptions about using calculators for trigonometric calculations.

Opening:

• Students will engage in a real-life scenario where they need to find the height of a tree using trigonometry.

• Question: How can we use trigonometric ratios and calculators to solve real-world problems like finding the height of objects?

Introduction to New Material:

• Explain the concept of trigonometric ratios (sine, cosine, tangent) and how they relate to right triangles.

• Demonstrate how to use a calculator to calculate trigonometric values for different angles.

• Discuss a common misconception where students may incorrectly apply trig ratios without understanding the context.

Guided Practice:

• Provide examples of right triangles and guide students through using their calculators to find missing sides using trigonometric ratios.

• Scaffold questioning by starting with simpler examples and gradually increasing the complexity.

• Monitor student performance by circulating the room and providing support where needed.

Independent Practice:

• Assign a set of right triangles for students to solve using trigonometric ratios and their calculators.

• Include a mix of different angles and side lengths to ensure mastery.

• Encourage students to show their work and explain their reasoning.

Closing:

• Have students share their solutions and explain their process for finding missing sides.

• Summarize the key points of using trigonometric ratios and calculators in solving right triangles.

Extension Activity:

• Challenge early finishers to create their own right triangle problems for a classmate to solve using trigonometric ratios.

Homework:

• Homework suggestion: Create a set of right triangles and solve for the missing sides using trigonometric ratios and a calculator.

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

• CCSS.MATH.CONTENT.HSG.SRT.C.8a: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.