Solving Trigonometric Equations

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Solving Trigonometric Equations
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First Degree Trigonometric Equations

• These are equations where there is one kind of
  trig function in the equation and that function
  is raised to the first power.

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Steps for Solving

• Isolate the Trigonometric function.
• Use exact values to solve and put answers in
  terms of radians.
• If the answer is not an exact value, then use
  inverse functions on your calculator to get
  answers

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Now figure out where sin -1/2 on the unit
circle.
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Complete the List of Solutions

• If you are not restricted to a specific interval
  and are asked to give the general solutions then
  remember that adding on any integer multiple of
  2p represents a co-terminal angle with the
  equivalent trigonometric ratio.

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Where k is an integer and gives all the
coterminal angles of the solution.
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Practice

• Solve the equation. Find the general solutions

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Second Degree Trigonometric Equations

• These are equations that have one kind of
  Trigonometric function that is squared in the
  problem.
• We treat these like quadratic equations and
  attempt to factor or we can use the quadratic
  formula.

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This is a difference of squares and can factor
Solve each factor and you should end up with 4
solutions
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Practice
Find the general solutions for
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Writing in terms of 1 trig fnc

• If there is more than one trig function involved
  in the problem, then use your identities.
• Replace one of the trig functions with an
  identity so there is only one trig function being
  used

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Solve the following
Replace cos2 with 1-sin2
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Solving for Multiple Angles

• Multiple angle problems will now have a
  coefficient on the x, such as sin2x1
• Solve the same way as previous problems, but
  divide answers by the coefficient
• For general solutions divide 2 by the
  coefficient for sin and cos. Divide by the
  coefficient for tan and cot.

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Find the general solutions for
sin 3x 2 1
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Practice