5.2 & 5.3

In these two sections we are solving equations for a variable, such as x. This is very similar to what we have done in previous years and sections. Except, we are adding the trigonomic ideas that we have been focusing on in the previous sections.

SIMILARITIES

We are still focusing on getting x by itself.
This means that the order of operations is the same- addition/subtraction first, then multiplucation/division, and finally parenthesis/exponents.

ex. of old equation ex. of new equation
2x-5=5 2cos(x)-5=5

DIFFERENCES

Now we have to use the ideas of sine, cosine, tangent, secant, cosecant, and cotangent.
The answers we get from these equations are angle measures from the unit circle.
Instead of getting one answer from a simple equation, we usually get multiple answers.

ex.
2cos(x)+1=0
2cos(x)=-1
cos(x)=-1/2
x=arccos(-1/2)
x=4π /3 x=2π /3

These new ideas use the concepts that we have already learned and incorporated them together.