This week in Precalc 11, I learned about reference angles and the CAST Rule.
I learned that for reference angles, they are angles that start from the x-axis and are less than 90 degrees, here is an example…
The angle of the rotation is 170 degrees, so I take 180 minus 170 which will leave me with a reference angle of 10 degrees.
Here is another example, the angle of rotation is 200 degrees so I take 200 and minus 180 which will leave me with a reference angle of 20 degrees.
In Quadrant one, the reference angle is the rotation angle, in Quadrant 2, it is 180 degrees minus the rotation angle, in quadrant 3, it is rotation angle minus 180 degrees, In Quadrant 4, the reference angle is the rotation angle minus 270 degrees. Now that we know how to calculate reference angle, we can now move onto the CAST rule.
When we are using triganomic functions in each quadrant, it is the easiest for us to have a positive numerator and denominator, so we need a certain trig function to help us achieve that. Here is where the CAST rule helps us. In Quadrant 4, we have C. This means that in order to have a positive answer, we must use Cos in this quadrant. In Quadrant 1, we have A, meaning that all trig functions in this quadrant will result in a positive answer. In Quadrant 2, we have S, meaning that we need to use Sin to in this quadrant to get a positive answer. And last, in Quadrant 4, we have T which requires us to use tan in order to get a positive answer.
Here is an example of finding an angle in quadrant 4. As we can see, using a trig function other than cos in this quadrant will result in a negative answer.
