This week in pre calc we started learning sine/cosine law. Learning these laws made trigonometry much easier and faster to do. The laws consist of different formulas made up to find either a missing side length or a missing angle in a triangle.
Sine law: For sine law to work you need to have an angle and the side length facing each other at least once, because without this you won’t have enough information to fill into the formula and will have too many unknowns, making it impossible. Another thing to be aware of is you need to check for the second triangle in quadrant II. How you do this is you take what the angle would be in quadrant II (180-__), and then add it up with your other angles. If it goes over 180 degrees you will reject the answer because we know that doesn’t make sense and can’t be possible.
Formula:
You don’t need to use all three options when solving for either the side length or the angle though, you need one fraction fully filled out as well as your fraction with your unknown.
Applied:
Cosine Law: Cosine law is a mesh of trig as well as the pythagorean theorem and you will see that when you look at it. Something to remember when using cosine law is when you’re solving for a side length, at the end, you need to square root your answer as well as b^2. Just like in pythagorean theorem your second last line of work needs to be square rooted because you can’t have what you’re solving for squared. When you’re solving for an angle using cosine law it is the equation to solve for a side length but rearranged algebraically. Something to note when solving for an angle is, when putting it into your calculator you need to put brackets on the top line of work as well as around the second line, just so your calculator doesn’t get confused and accidentally give you the wrong answer or an error.
Formula:
Applied:
These two new laws that we have learnt, in my opinion has made trig this year much easier and make much more sense for me. It’s just a matter of labeling everything properly, which if you weren’t sure how, you label the side length across from the angle the same thing. So if angle A was facing a side length it would now become side a. It’s more a thing of punching it into your calculator properly.