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7.1 Basic Trigonometric Identities

7.1 Basic Trigonometric Identities. Identities are equations that are true for all input values. Example:. Reciprocal Identities. The following trigonometric identities hold for all values of  where each expression is defined. Memorize these. Quotient Identities.

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7.1 Basic Trigonometric Identities

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  1. 7.1 Basic Trigonometric Identities Identities are equations that are true for all input values. Example:

  2. Reciprocal Identities The following trigonometric identities hold for all values of  where each expression is defined. Memorize these.

  3. Quotient Identities The following trigonometric identities hold for all values of  where each expression is defined. Pythagorean Identities

  4. Prove the equation is not an identity Proving that the equation is not an identity can be done by finding a counter example. Example: Let  = 0.

  5. Use the given information to determine the exact trigonometric value. Use an identity to change cosine into secant.

  6. Use the given information to determine the exact trigonometric value. Use an identity to change sine into cosine.

  7. Express the Value as a Trigonometric Function of an Angle in Quadrant I 1. If needed add or subtract 2 in order to fall between 0 and 2 2. Determine the reference angle and quadrant. 3. Rewrite as the same trig. Function of the reference angle. Give an appropriate sign (+ or -). Cosine is negative in Q3.

  8. Express the Value as a Trigonometric Function of an Angle in Quadrant I 1. If needed, add or subtract 360 in order to fall between 0 and 360 2. Determine the reference angle and quadrant. 3. Rewrite as the same trig. Function of the reference angle. Give an appropriate sign (+ or -). Sine is positive in Q1, thus cosecant is positive.

  9. Simplify (fewer terms and trig. functions) Use identities to substitute in such a way that the expression can be simplified as far as possible. One method is to rewrite each trig. function in terms of sine and cosine.

  10. Simplify (fewer terms and trig. functions) Use identities to substitute in such a way that the expression can be simplified as far as possible.

  11. Simplify (fewer terms and trig. functions) Use identities to substitute in such a way that the expression can be simplified as far as possible. Keep a sharp eye out for Pythagorean identities.

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