This week in Precalc 11, we continued off what we started on trigonometry before our winter break. Since me not doing the week 16 blog post, I have learned a lot about trigonometry this semester that I haven’t share yet. One of the biggest thing we learned was special triangles and the unit circle. If the angle given is a part of a special triangle we can use the specific trig ratio for that triangle and we can use the unit circle for our 0, 90, 180, 270 and 360 angle.


ASTC : ALL STUDENTS TAKE CALCULUS (a way to remember where sin, cos and tan are positive or negative in each quadrant)


  • COSINE :
    • finding side :a^2 = b^2 + c^2 - 2bcCOSA
    • finding angle : COSA = \frac{b^2+c^2-a^2}{2bc}
  • SINE :
    • finding side : \frac{a}{SINA} = \frac{b}{SINB} = \frac{c}{SINC}
    • finding angle :\frac{SINA}{a} = \frac{SINB}{b} = \frac{SINC}{c}

What I found the most important when doing sine and cosine law was that you needed to know where to locate the opposite. So if your angle B is showing on the diagram, the opposite from that angle is your b side which is shown. Then figuring out to use sine, cosine or primary trig ratios is your next step and it all depends on the information that is given. If its a right triangle you can use primary trig ratios, if you have at least one complete fraction like below, you can use sine law. If there isn’t enough information for sine law you can use cosine law but in the case where there are only angles given, you can not solve the triangle because there isn’t enough information. Drawing diagrams and once again knowing how the angle and sides work together is a big part of trig this year.

Ex :

If we understand when to use cosine and sine law, we can plug in the numbers into the formula to figure out either the angle or the side

picture used :