Hello, I was practicing for my upcoming SAT and I happened to find a problem in the no calculator math section.
They asked for the value of cos(180 degrees) I am not sure how to solve this without a calculator and I was wondering if I need to memorize this for the SAT or if there’s an explanation. Thankyou
@scaredjunior55 cos(180°) = -1.
The best way to memorize those values is to familiarize yourself with the [unit circle](Unit circle - Wikipedia). For trig functions, we define 0° as in the positive x-axis and increasing when you go counterclockwise - so (0,1) corresponds to 90°, (-1,0) corresponds to 180°, etc. (Wikipedia explains this). Then:
The x-coordinate of any point on the unit circle corresponds to the cosine of the corresponding angle.
The y-coordinate of any point on the unit circle corresponds to the sine of the corresponding angle.
If you have learned sin, cos, tan and other trig functions in terms of ratios of side lengths in right triangles, you should see that these two definitions are completely consistent with one another. However you have to be careful with sign.
For SAT purposes, it may help to memorize sin, cos, tan of 0°, 30°, 45°, 60°, 90° and similar angles (can be referenced using 30-60-90 and 45-45-90 right triangles) - however that is not an exhaustive list of all the trig that might be covered.
I also find it helpful to memorize the sine and cosine of the quadrantal angles. Or, memorize the basic shape of the corresponding graphs. If you draw some quick-and-dirty graphs, you can see that:
sin (0°) = 0
sin (90°) = 1
sin (180°) = 0
sin (270°) = -1
sin (360°) = 0
While
cos (0°) = 1
cos (90°) = 0
cos (180°) = -1
cos (270°) = 0
cos (360°) = 1