This week in math, we started the trigonometry unit. In my opinion, the two most crucial aspects of this unit are knowing how and when to use sin and/or cosine law.
SIne Law: Although you could use sine law for any triangle, it is essentially a way to determine a side or angle of a triangle in which you couldn’t use SOH CAH TOA, a non-right triangle. Sine law has two principal versions of the formula; one in which you would use to find a missing angle, and the reciprocal of that would be used to find a missing side.
To find an angle:
To find a side:
To know which of the two versions of the formula to use, you need to remember that your variable must be in the numerator.
Here’s an example: “Determine the measure of 
- Using the formula, we can fill out the information we know and we will use the formula with the angles in the numerator because that’s what we’re looking for.
- Next we can eliminate the portion of the formula that we do not need:
- Now we can finish solving:
Cosine Law: Much alike sine law, cosine law will solve for any triangle, however, unlike sine law, you do not need to know aside and the opposite angle (one full fraction in the formula is required).
Cosine Law looks like this:
You can rearrange the formula to solve for any variable, but the leftmost term and the cosine variable must be the same variable.
Here’s an example: “Solve for c”
- First, we can input the information we know into the formula.
- Unlike Sine Law, there is no portion of the equation we can eliminate.
- Now we can finish solving by isolating the variable:
