2. Solving Trigonometric Equations Involving Multiple Angles 6.3 JMerrill, 2009

3. 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

4. Example Solve cos 2x = 1 – sin x for 0 ≤ x < 2π

5. You Do Solve for 0 o ≤θ<360 o cos 2x = cos x

6. Example Solve 3cos2x + cos x = 2 for 0 ≤ x < 2π

7. Example Solve 2sin2x = 1 for 0 o ≤ θ < 360 o Pretend the 2 isn’t in front of the x and solve it (solve sin x = ½ ) All of the previous examples were solved for x. Now we’ll solve for 2x directly.

8. You Do Solve for 0 o ≤θ<360 o tan 2 2x-1=0