# Using Fundamental Identities

## Presentation on theme: "Using Fundamental Identities"— Presentation transcript:

Using Fundamental Identities
Objectives: Recognize and write the fundamental trigonometric identities Use the fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions, and rewrite trigonometric expressions

WHY??? Fundamental trigonometric identities can be used to simplify trigonometric expressions, such as for the coefficient of friction.

Fundamental Trigonometric Identities
Reciprocal Identities Quotient Identities

Fundamental Trigonometric Identities
Pythagorean Identities Even/Odd Identities

Fundamental Trigonometric Identities
Cofunction Identities

Example: If and Ө is in quadrant II, find each function value.
a) sec Ө To find the value of this function, look for an identity that relates tangent and secant. Tip: Use Pythagorean Identities.

Example: If and Ө is in quadrant II, find each function value. (Cont.)
b) sin Ө c) cot (- Ө ) Tip: Use Quotient Identities. Tip: Use Reciprocal and Negative-Angle Identities.

2. Use the values cos x > 0 and identities to find the values of all six trigonometric functions. What quadrant will you use? 1st quadrant

Using Identities to Evaluate a Function
Use the given values to evaluate the remaining trigonometric functions (You can also draw a right triangle)

Simplify an Expression
Simplify cot x cos x + sin x. Click for answer.

Example: Simplify 1. Factor csc x out of the expression.

2. Use Pythagorean identities to simplify the expression in the parentheses.

3. Use Reciprocal identities to simplify the expression.

Simplifying a Trigonometric Expression

Factoring Trigonometric Expressions
Factor the same way you would factor any quadratic. If it helps replace the “trig” word with x Factor the same way you would factor

Make it an easier problem.
Let a = csc x 2a2 – 7a + 6 (2a – 3)(a – 2) Now substitute csc x for a.

1. Use Pythagorean identities to get one trigonometric function in the expression.

2. Now factor.

Factoring Trigonometric Expressions

More Factoring

Adding Trigonometric Expressions (Common Denominator)