This week in Pre-cal 11 we learned Trigonometry again, the difference in comparison to the pervious knowledge we learned in grade 10 are, now SOHCAHTOA, works in all 360 degrees and we learned two new laws: the sine and cosine law which comes in handy when there isn’t enough information for SOHCAHTOA.
And this is how trig ratio is possible for all angles<360. I was introduced to this circle, with have 4 quadrants, basically, the x-axis of it is the principal axis and there are two angles, one is the rotation angle, the angle of that is measured from the X axis in the top right quadrant, the quadrant one, and the angle between that and the X-axis is the reference angle and the reference angle have the same trig ratio as the rotation angle, but it might be negative. And how do you determine if a rotation angle in a certain quadrant is negative with its trig ratio, there is something called the CAST rule, with that you can easily determine if your trig ratio is positive or negative.
This is the Cosine law, it can determine an angle with the length of the two sides created it known, vice versa you can find the any of the side lengths with the angle and when the other side is known as well.
The is the Sine Law, it can determine any angle or sides in a triangle with two sets of side and the angle opposite of it, using the ratio one can cross multiply and solve to find any one of these variables with other three.