Exploring Sine, Cosine, and Tangent

Objective:

Students will be able to define and calculate the sine, cosine, and tangent of angles in right triangles.

Assessment:

Students will complete a worksheet where they have to calculate the values of sine, cosine, and tangent for given angles in right triangles.

Key Points:

• Definition of sine, cosine, and tangent

  • Sine Ratio: The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

    • Formula: sin(θ) = Opposite/Hypotenuse

  • Cosine Ratio: The cosine of an angle in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

    • Formula: cos(θ) = Adjacent/Hypotenuse

  • Tangent Ratio: The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

    • Formula: tan(θ) = Opposite/Adjacent

• How to calculate sine, cosine, and tangent in a right triangle

• Relationship between the angle measures and the ratios

Opening:

• Start the lesson by introducing the concept of sine, cosine, and tangent using real-life examples involving angles and right triangles.

• Engage students with a question like, "Can you think of situations where knowing the sine, cosine, or tangent of an angle would be useful in solving problems?"

Introduction to New Material:

• Define sine, cosine, and tangent clearly.

• Explain how to calculate each ratio in a right triangle.

• Address a common misconception such as "Thinking that sine is always greater than cosine or tangent."

Guided Practice:

• Provide examples for students to practice calculating sine, cosine, and tangent ratios in right triangles.

• Scaffold questions from basic to more complex to ensure understanding.

• Monitor student performance by walking around the classroom and providing guidance as needed.

Independent Practice:

• Assign a set of problems where students have to find the sine, cosine, and tangent of specified angles in right triangles.

• Clearly outline the steps for solving each problem.

• Encourage students to ask questions if they encounter difficulties.

Closing:

• Have students share their answers and discuss the results as a class to recap the key concepts learned.

Extension Activity:

• For early finishers, provide additional challenging problems where students have to apply the concepts of sine, cosine, and tangent in different types of triangles.

Homework:

• Create homework questions where students have to find the unknown sides or angles in right triangles using sine, cosine, and tangent ratios.

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: Apply the primary trigonometric ratios of sine, cosine, and tangent to determine unknown angle measures in right triangles.