5.1 Using Fundamental Identities

5.1 Using Fundamental Identities

Integrated Math 3 Honors

Mr. Washington

Objectives

• Recognize and write the fundamental trigonometric identities.

• Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions. 

Uses for Trigonometric Identities

• To Evaluate Trig Functions

• Simplify Trig Expressions

• To Develop Additional Trig Functions

• To Solve Trig Equations

Fundamental Trigonometric Identities

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Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Multiple Choice

Simplify

 $\csc^2x\left(1-\cos^2x\right)$  

• 1

• Already simplified

• -1

Solution

Multiple Choice

 $\frac{\cot^2x}{\csc^2x}$  Simplify

•  $\cot^2x$  

•  $\sin^2x$  

•  $\cos^2x$  

•  $\sec^2x$  

Solution

Multiple Choice

 $\frac{1}{1+\cos^2\theta}$  

•  $\sin^2x$  

•  $\cos^2x$  

•  $\sec^2x$  

Solution

Multiple Choice

 $\csc\ t\ +\ \tan\ t\ +\sec t$  

• 1 sec t

• 2 sec t

• 3 sec t

• 4 sec t

Solution