This week in Precalc 11 we started Trigonometry and learning about angles in all quadrants, where in Math 10 we only used quadrant one to solve angles. We started by changing SOH CAH TOA into its new form. Sinθ=y/r, Cosθ=x/r, Tanθ=y/x. Since we have started using all quadrants, when we have to solve for theta we will have 2 answers. We learned an acronym for memorizing where each ratio is positive and negative, All Students Take Calculus. This acronym is to show which ratios are positive in each quadrant. This is important to know because when you are solving for theta there are always going to be two different answers.

This is what it looks like when graphed:

The A means that all the ratios are positive in the first quadrant, S means that only sine is positive, T means only tangent is positive and C means that only cosine is positive in that quadrant.

This is useful to know when you are trying to solve for theta and you are tying to figure out if you are finding where the ratio is positive or negative.

If you were given this question, sinθ=0.63, you would first look at your ASTC graph and find where sine is positive, which is quadrant one and two. Then you would put it into your calculator and get an angle which is less that 90° and that is your reference angle for all quadrants and it is your rotation angle in quadrant one. The first angle is 39° and to find the next one you have to do 180°-39° to find the next angle. So your final answers will be 39° and 141°.