Solving Trigonometric Equations Involving Multiple Angles 6.3

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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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### SolvingTrigonometric EquationsInvolving Multiple Angles6.3

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
• 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
• Solve cos 2x = 1 – sin x for 0 ≤ x < 2π
You Do
• Solve for 0o≤θ<360o

cos 2x = cos x

Example
• Solve 3cos2x + cos x = 2 for 0 ≤ x < 2π
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 Do
• Solve for 0o≤θ<360o

tan22x-1=0