1. Chapter 4 Analytic Trigonometry Section 4.5 More Trigonometric Equations

2. If a more complicated angle is inside the sine or cosine there is one more step of solving for x at the end. The example to the right is how to solve: 1. Draw unit circle. 2. Draw horizontal or vertical line the correct distance on x or y axis. 3. Find angles where line hits the unit circle. 4. Add 2 k  to each angle. 5. Solve for x. Solutions: The Equations: a sin x + b = c and a cos x + b = c If the sine or cosine is not isolated (i.e. all by itself on one side of the equation) carry out the algebra to isolate the sine or cosine. Solve: Now apply what we did above to get the solutions. Solutions:

3. Simplifying Equations Before Solving Some times equations might need to be simplified using a combination of trigonometric identities and algebra before solving them. Regroup: Factor: Solve each equation Give answers in radians.

4. Equations with Powers of Sine or Cosine If the equation you are trying to solve has a power of sine or cosine, set one side equal to zero and factor the other side. Use what was just discussed to solve the parts you get. Solve: Solutions: Solve: Solutions: No Solutions (first equation)

5. Rearrange Square both sides Regroup Apply Identity Cancel

6. Equations With Both Sine and Cosine If a trigonometric equation has both a sine and cosine in it use trigonometric identities to change it to an equation involving either all sine or all cosine. Solve: Find the other angle. 360  -36.8699  =323.13  The solutions for this are: