7.5 Trig Equations

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!

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

Process: Z(FSR)BS

• Zero, Factor, Simplify, Replace, Break up, Solve

• Zoey Finds Snow Really BotherSome

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

Step 2: Factor

Sin(x)cos(x) - ½cos(x) = 0

Factor out Cos(x)

Cos(x){sin(x)- ½} = 0

Step 3: Simplify

Cos(x){sin(x)- ½} = 0

Can this be simplified?

No!

Step 4: Replace

Cos(x){sin(x)- ½} = 0Can anything be replaced by another identity?

No!

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

Step 6: Solve

Cos(x) = 0 and Sin(X) - ½ = 0

Cos(X) = 0 when X = 90°

Step 6 continued

Sin(X) - ½ = 0 Sin(X) = ½Sin(X) = ½ when X = 30 °

Bibliography

• http://www.freemathhelp.com/trig-double-angles.html

• Glencoe, Advanced Mathematical Concepts, textbook