Mastering Trig Differentiation

Mastering Trig Differentiation

Learning Objective

At the end of the lesson, you will be able to differentiate trigonometric functions using various differentiation rules.

What do you already know about trigonometric functions and their derivatives?

Trigonometric Functions

Trigonometric functions include sine, cosine, and tangent.

Derivatives of Trigonometric Functions

Derivative of sine function: cos(x), derivative of cosine function: -sin(x), derivative of tangent function: sec^2(x)

Differentiation Rules

Use the chain rule, product rule, and quotient rule to differentiate trigonometric functions combined with other functions.

Examples

Differentiate sin(2x), differentiate cos(3x^2), differentiate tan(4x)/x

Trigonometric Identities

Trigonometric identities, such as the Pythagorean identities, can be useful in simplifying trigonometric functions before differentiation.

Practice Problems

Solve the following differentiation problems: a) differentiate cos(5x) + sin(2x), b) differentiate tan(3x^2) - cos(2x), c) differentiate sec(x) * tan(x)

Summary

Recap the key concepts learned in this lesson: trigonometric functions, derivatives, differentiation rules, and trigonometric identities.

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.