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Solving Trigonometric Equations Involving Multiple Angles 6.3. JMerrill, 2009. Strategies for Solving Trig. Equations with Multiple Angles. If the equation involves functions of 2x and x, transform the functions of 2x into functions of x by using identities

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Solving trigonometric equations involving multiple angles 6 3

SolvingTrigonometric EquationsInvolving Multiple Angles6.3

JMerrill, 2009


Strategies for solving trig equations with multiple angles
Strategies for Solving Trig. Equations with Multiple Angles

  • If the equation involves functions of 2x and x, transform the functions of 2x into functions of x by using identities

  • If the equation involves functions of 2x only, it is usually better to solve for 2x directly and then solve for x

  • Be careful not to lose roots by dividing off a common factor

  • Remember: You can always graph to check your solutions


Example
Example

  • Solve cos 2x = 1 – sin x for 0 ≤ x < 2π


You do
You Do

  • Solve for 0o≤θ<360o

    cos 2x = cos x


Example1
Example

  • Solve 3cos2x + cos x = 2 for 0 ≤ x < 2π


Example2
Example

All of the previous examples were solved for x. Now we’ll solve for 2x directly.

  • Solve 2sin2x = 1 for0o ≤ θ < 360o

Pretend the 2 isn’t in front of the x and solve it (solve sin x = ½ )


You do1
You Do

  • Solve for 0o≤θ<360o

    tan22x-1=0