Lesson 2: 5.2 Verifying Trigonometric Identities

How do you verify a trigonometric identity?

identity

HSF-TF. B. 6 - Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

Use Khan Academy resources.

Students will use their prior knowledge to think abstractly in order to verify trigonometric identities. Similar to writing a proof in geometry, students will know what they should obtain when verifying a trigonometric identity.

You can use trigonometric identities to rewrite trigonometric expressions. For instance, trigonometric identities can be used to simplify an equation that models the length of a shadow cast by a gnomon (a device used to tell time).

Students often try to verify identities by using methods learned for solving equations. Emphasize that identities are not conditional equations but two equivalent expressions. Either side must be worked on separately as an expression. Each step should have a justifiable reason for the changes made. Writing the reasons can help students understand the process.
Some students may make errors when substituting a trigonometric identity due to a lack of parentheses.

You may want to encourage your students to identify the reasoning behind each solution step in the examples in this section while covering the comment lines. This should give them practice in recognizing the fundamental trigonometric identities.

Use common assessments.

Pre-Calculus with Limits resources.