1. 7.5 Trig Equations

2. The Story! In the arctic, zoey wants to know how to dress! She has to dress differently depending on the temperature of the snow (degrees). Find the temperature (degrees) in each equation!

3. The process: How to find the temperature (X) Find a way to get your equation to equal zero (some equations already will, others will require changing the terms of the equation so that all of the variables are on one side and a zero is on the other side of the = sign) After getting it to zero, see if anything can be factored, simplified, or replaced by an identity. This will help you get X all alone. Break the parts of the equation up into terms of X Solve each part for X and test the solutions in the original equation

4. Process: Z(FSR)BS Zero, Factor, Simplify, Replace, Break up, Solve Zoey Finds Snow Really BotherSome

5. Example Sin(x)Cos(x) = ½cos(x) Step 1: Zero Set equation equal to zero Sin(x)cos(x) = ½cos(x) - ½cos(x) - ½cos(x) Sin(x)cos(x) - ½cos(x) = 0

6. Step 2: Factor Sin(x)cos(x) - ½cos(x) = 0 Factor out Cos(x) Cos ( x ) {sin ( x ) - ½} = 0

7. Step 3: Simplify Cos ( x ) {sin ( x ) - ½} = 0 Can this be simplified? No!

8. Step 4: Replace Cos ( x ) {sin ( x ) - ½} = 0 Can anything be replaced by another identity? No!

9. Step 5: Break Up Cos ( x ) {sin ( x ) - ½} = 0 Break up the cos and the sin parts of the equation Cos(x) = 0 and Sin(X) - ½ = 0

10. Step 6: Solve Cos(x) = 0 and Sin(X) - ½ = 0 Cos(X) = 0 when X = 90°

11. Step 6 continued Sin(X) - ½ = 0 Sin(X) = ½ Sin(X) = ½ when X = 30 °

12. Bibliography http://www.freemathhelp.com/trig-double- angles.html http://www.freemathhelp.com/trig-double- angles.html Glencoe, Advanced Mathematical Concepts, textbook