Trigonometry: Solving Simple Math Questions

• Mathematics
• Upper Secondary (Key Stage 4)
• GCSE

Trigonometry: Solving Simple Math Questions

Learning Objective

At the end of the lesson you will be able to answer simple math questions on trigonometry.

Introduce the learning objective and explain to students what they will learn in this lesson.

What do you already know about trigonometry?

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of triangles.

Introduce the definition of trigonometry and explain its relevance in solving math problems.

Trigonometric Functions

Trigonometric functions include sine, cosine, and tangent.

Explain the three basic trigonometric functions and their relationship to right triangles.

Sine Function

The sine function is defined as the ratio of the length of the side opposite an angle to the length of the hypotenuse.

Explain the sine function and provide an example of how to use it to solve a math problem.

Cosine Function

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Explain the cosine function and provide an example of how to use it to solve a math problem.

Tangent Function

The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Explain the tangent function and provide an example of how to use it to solve a math problem.

Pythagorean Theorem

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

Explain the Pythagorean theorem and how it can be used in solving trigonometry problems.

Inverse Trigonometric Functions

Inverse trigonometric functions are used to find the angle given the ratio of the sides.

Introduce the concept of inverse trigonometric functions and provide an example of how to use them.

Example Problem 1

Find the value of sin(30°).

Provide an example problem using the sine function and guide students through the steps to solve it.

Example Problem 2

Find the value of tan(45°).

Provide an example problem using the tangent function and guide students through the steps to solve it.

Example Problem 3

Find the value of cos(60°).

Provide an example problem using the cosine function and guide students through the steps to solve it.

Example Problem 4

Find the value of x in the right triangle given that the two legs are 3 and 4.

Provide an example problem using the Pythagorean theorem and guide students through the steps to solve it.

Example Problem 5

Find the value of θ in the right triangle given that the adjacent side is 4 and the hypotenuse is 5.

Provide an example problem using inverse trigonometric functions and guide students through the steps to solve it.

Review

Review the basic concepts of trigonometry and the different functions.

Summarize the main points of the lesson and ask students if they have any questions.

Practice Problems

Provide a set of practice problems for students to solve.

Give students time to work on the practice problems and provide assistance as needed.

Answer Key

Provide the answer key for the practice problems.

Review the answers to the practice problems with students.

Real-Life Applications

Discuss the real-life applications of trigonometry such as architecture, engineering, and physics.

Engage students in a discussion about how trigonometry is used in everyday life.

Conclusion

Summarize the main concepts learned in the lesson and encourage students to continue practicing.

End the lesson by summarizing the main points and encouraging students to continue practicing.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.