SAT Physics no calculator, but trigonometric functions?

rspence
Sat, 20 Oct 2012 11:03:20 +0000

You should at least know sine and cosine of angles that are multiples of π/6 and π/4. This requires knowing the 30-60-90 and 45-45-90 triangles.

To find sin(π/3) quickly in your head, visualize a unit circle with a terminal angle of π/3 (60 deg). The ray corresponding to pi/3 will intersect the unit circle at some point.

The sine of the angle is simply the y-coordinate of that point (sin θ = y/r = y because r = 1). The cosine of the angle is the x-coordinate of that point. For π/3, the corresponding point on the unit circle is (1/2, √3/2), so cos (π/3) = 1/2.

In general, for a unit circle with radius r = 1,
sin θ = y
cos θ = x
tan θ = y/x.