# Week 15 – Math 11

For the fourteenth week of Preacul 11, we started a new chapter —Trigonometry.  In grade 11 trig there are way more things to learn and the simplicity of SOH CAH TOA won’t cut it for grade 11 trig.

In this new trig we learn that there are 4 quadrants, it’s different from what we learned in grade 10. In grade 10 we were doing trig in quadrant 1 for most of the time, and we know this because Sine, Cosine and tangent were all positive in quadrant 1. Another thing that we learned was Sine Law, Sine law is a way that we can use to find a certain angle or length of something.

For example, for a Triangle ABC from A to B it’s 8.6; from A to C it’s 6.1; Angle C is 65°. Now, we are trying to find the length of BC.

You would use the equation of $\frac{A}{SinA} = \frac{B}{SinB} = \frac{C}{SinC}$ , this is for when you’re looking a missing side but for a missing angle,  and the equation $\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$ it’s the same equation just flipped. And what we need to do right now is to find the angle of B, so it can help us find the side length of BC so you would use the equation of  $\frac{SinA}{A} = \frac{SinB}{6.1} = \frac{Sin65}{8.6}$ . Now we would use the two fractions that are filled in the most so now the equation would be $\frac{SinB}{6.1} = \frac{Sin65}{8.6}$ .  To solve this equation is to basically isolate the B and put everything else on one side so the equation and solve from there which would give the angle B 40°, and from there you would keep using the same equation to find side BC.  This is how you use the Sine Law.