Sec' 7'1 Trigonometric Identities

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• Sec. 7.1 Trigonometric Identities
• Sec. 7.2 Addition and Subtraction Formulas
• In this chapter, we will be simplifying and
  factoring expressions that involve trigonometric
  functions.
• To do this we will need to use a number of
  trigonometric identities and formulas.

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Graphs of Trig Functions
Sin(x) Cos(x) Tan(x) Csc(x) Sec(x) Cot(x)
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• Reciprocal Identities
• Pythagorean Identities

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• Even - Odd Identities
• Cofunction Identities

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• Guidelines for Proving New Identities
• Start with one side of the equation.
• Use known identities to transform that side to
  make it equal to the other side.
• Try some of the following ideas if you are stuck
• Get common denominators
• Change all trig functions to sin and cos.
• Keep in mind the expression that is your goal.
• Be careful not to do the same thing to both
  sides of the equation. With trig functions, it
  is easier to accidentally turn a false statement
  into a true one by doing this.

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• Prove the following

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• Prove the following

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• Prove the following

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• Prove the following

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• Prove the following

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• Prove the following

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• Prove the following

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• Prove the following

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• Addition and Subtraction Formulas

Well show a visual proof of this on Friday. The
book has an algebraic proof.
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• How to use Addition and Subtraction Formulas
• Use the following identity
• To show the cofunction identity

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• How to use Addition and Subtraction Formulas
• Using the values of the trig functions at certain
  angles, we can determine the values at new
  angles.

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• If Sin(x)1/3, and x is in the 2nd quadrant,
  draw a rough sketch of the angle and find the
  exact values of