Verifying Trigonometric Identities

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Verifying Trigonometric Identities

• Section 5.2
• Math 1113
• Created Presented by Laura Ralston

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Verifying Trigonometric Identities

• In this section, we will study techniques for
  verifying trigonometric identities.
• The key to verifying identities is the ability to
  use the fundamental identities and rules of
  algebra to rewrite trigonometric expressions

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Review

• Algebraic Expression a collection of numbers,
  variables, symbols for operations, and grouping
  symbols contains no equal sign
• 2(4x -3) 6
• 2sin(4x p) 3

• Equation a statement that two mathematical
  expressions are equal.
• x 2 5
• sin x 0

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Three Categories of Equations

• Contradiction no values of the variable make
  the equation true
• x 2 x
• sin x 5

• Conditional only 1 or several values of the
  variable make the equation true
• x 2 5 ---- x 3
• sin x 0 ----- x 0

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• Identity equation is true for EVERY value of
  the variable
• x x 2x cos2x sin2x 1
• 2x 2x

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• Verifying an Identity is quite different from
  solving an equation.
• There is no well-defined set of rules to follow
  in verifying trigonometric identities and the
  process is best learned by practice!!!

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Guidelines for Verifying Trig Identities

• Work with one side of the identity at a time. It
  is often better to work with the more complicated
  side first.
• Look for opportunities to factor an expression,
  add fractions, square a binomial, or create a
  monomial denominator.

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• Look for opportunities to use the fundamental
  identities. Note which functions are in the
  final expression you want.
• Sines and cosines pair up well, as do secants and
  tangents, and cosecants and cotangents.

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• If all else fails, try converting all terms to
  sines and cosines.
• Always try something!! Even paths that lead to
  dead ends give you insights.

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• There can be more than one way to verify an
  identity. Your method may differ from that used
  by your instructor or classmates.
• This is a good chance to be creative and
  establish your own style, but try to be as
  efficient as possible.