Do Now Solve for x: 1. x + 3x – 4 = 2x – 7 2. (x + 1)2 – 3 = 4x + 1

Verifying Trigonometric Identities Section 5.2 Verifying Trigonometric Identities Objective: SWBAT to verify a Trigonometric Identity working with one side of the equation.

Word Identities In order to do many of the operations and processes in mathematics we need to follow certain rules. There are rules for addition, subtraction, multiplication, division, decimals, solving equations, proving trig identities…. RULE: Change ONLY one letter at a time and form a new word at each step.

Word Identities RULE: Change ONLY one letter at a time and form a new word at each step. Change TEN to TWO… TEN T ___ N T o ___ Tw ____

Word Identities RULE: Change ONLY one letter at a time and form a new word at each step. Change TEN to SIX… TEN T ___ N Si___ SIX

Simplifying Equations and Verifying Identities Verifying identities means to demonstrate that two expressions represent the same thing. This allows you to replace one expression with another to help in simplifying.

Here are some equivalent terms; which is more simple A or B? 1 B. sin2 θ + cos2 θ A. sin θ/cos θ B. tan θ 1/sec θ B. cos θ A. 1+ tan2 θ B. sec2 θ

Hints for Verifying Identities 1. Learn the fundamental identities given in the last section. Whenever you see either side of a fundamental identity, the other side should come to mind. Also, be aware of equivalent forms of the fundamental identities. For example is an alternative form of the identity Try to rewrite the more complicated side of the equation so that it is identical to the simpler side. It is sometimes helpful to express all trigonometric functions in the equation in terms of sine and cosine and then simplify the result.

Hints for Verifying Identities…. 4. Usually, any factoring or indicated algebraic operations should be performed. The sum or difference of two trigonometric expressions such as can be added or subtracted in the same way as any other rational expression. 5. As you select substitutions, keep in mind the side you are changing, because it represents your goal. For example, to verify the identity try to think of an identity that relates tan x to cos x. In this case, since and the secant function is the best link between the two sides.

Hints for Verifying Identities…. 6. If an expression contains 1 + sin x, multiplying both the numerator and denominator by 1  sin x would give 1  sin2 x, which could be replaced with cos2x. Similar results for 1  sin x, 1 + cos x, and 1  cos x may be useful. Remember that verifying identities is NOT the same as solving equations.

Keep in Mind! These problems take practice to get good at them! Even if you are stumped, try something! Even a path that leads to a dead end can provide valuable insight.

Working with One Side Prove the identity

Working with One Side Solution—start with the right side

Working with One Side Prove the identity Start with the left side.

Working with One Side Prove the identity tan x sin x + cos x = sec x