FUNDAMENTAL Trigonometric IDENTITIES.

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Presentation transcript:

FUNDAMENTAL Trigonometric IDENTITIES

Trigonometric Identity A Trigonometric Identity is a trigonometric equation that is true for all values of the variables for which the expressions in the equation are defined.

Reciprocal Identities

Reciprocal Identities

Reciprocal Identities k odd integer

Reciprocal Identities k odd integer k an integer

Reciprocal Identities k odd integer k an integer k an integer

Reciprocal Identities k odd integer k an integer k an integer

We Could Also Say

Reciprocal Identities

Reciprocal Identities

Ratio Identities

Ratio Identities Recall The Unit Circle

1

1

1

1

1

1

1

1

1

1

1

1

1

1

Ratio Identities k odd integer

Ratio Identities k odd integer k an integer

Pythagorean Identities

Pythagorean Identities 1

Pythagorean Identities 1

Pythagorean Identities 1

Pythagorean Identities 1

Pythagorean Identities 1

Pythagorean Identities 1

Pythagorean Identities 1

Pythagorean Identities 1

Pythagorean Identities 1

Pythagorean Identities Most Important!! Most Important!! Most Important!!

Pythagorean Identities Other Two

Proof of the Indentity

What Are Proofs? A proof of an identity may be written using a vertical line to separate the expressions to be proved equivalent. Use known algebraic and trigonometric identities to replace on the expressions with an equivalent express. Repeat the process until an expression is obtained that is the same as that on the other side of the line DO NOT Add, Subtract, Multiply or Divided Both Sides by the Same Thing.

USE

Common Denominator

QED

quod erat demonstrandum QED   quod erat demonstrandum  Meaning "which was to be proved"

Proof of the Indentity

USE

Common Denominator

QED

quod erat demonstrandum QED   quod erat demonstrandum  Meaning "which was to be proved"

Odd-Even Identities

Odd-Even Identities Recall

Odd-Even Identities Odd Even

Odd Identities

Even Identities

Proof

Where's