Trigonometric EquationsPart 2

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Trigonometric EquationsPart 2

• 6.8

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Steps for Solving Basic Equations

• Solve the equation for the trigfunction(angleequat
  ion) that is in the equation. This trig function
  could be sin, cos,tan,cot,csc, or sec. The trig
  function might also be squared.
• Basic algebra should work here, although there
  will be times when taking the square root of both
  sides will complete the solving. Do not forget
  the plus or minus when taking the square root.

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Steps for Solving Basic Equations

• Now find the angles whose trigfunction(angleequati
  on) is the ratio indicated.
• Use a chart of the basic trig values, the unit
  circle, and/or a picture of the quadrantal angles
  to help.
• Remember that there may be more than one angle
  that meets the criteria, so find all the
  possibilities.
• Find the angles that work within one trip around
  the unit circle. Then add successive multiples
  of 2pi to each one to make a list of the
  possibilities.

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Steps for Solving Basic Equations

• Set angleequation equal to each angle.
• If angleequation is just theta, then the angles
  found are the answer to the problem only using
  the ones that belong in the specified interval.
• If angleequation is not just theta, then take
  each angle and set it equal to angleequation.
• Set angleequation equal to each angle and solve
  for theta. If there is an interval make sure
  that the final result does not exceed the
  interval.

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Steps for Solving Trig Equations

• If the equation has more than one trig function
  in it, then choose one of the following methods
  to rewrite the equation so it has only one trig
  function.
• FOIL
• Use a trig identity to rewrite.
• Distribute.

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Steps for Solving Trig Equations

• Let x trigfunction(?). Choose the trig function
  that you see in the equation.
• Now rewrite the equation in terms of x.
• Now factor the equation and solve for x.
• Now place trigfunction(?) back in for x.

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Steps for Solving Trig Equations

• Now find the angle whose trigfunction(?) is the
  ratio indicated.
• Create a chart of the basic trig values and a
  picture of the quadrantal angles to help.
• Remember that there may be more than one angle
  that meets the criteria, so find all the
  possibilitiesthe unit circle should help here.

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Examples

• 6,10, 12,14,