not sure there is any RIGHT equalities to know...but here are some that I memorized
sin (x) = cos (x + 90) [for degrees only]
cos (x) = cos (x - 90) [for degrees only]
sin (x) = 1/cot (x)
cos (x) = 1/sec (x)
tan (x) = 1/csc (x)
sin^2 (x) + cos^2 (x) = 1
Sin (x) Csc (x) Cos (x) Sec (x) Tan (x) Cot (x)
Quadrant 1
(0-90 degrees) + + + + + +
Quadrant 2
(90-180 degrees) + + - - - -
Quadrant 3
(180-270 degrees - - - - + +
Quadrant 4
(270-360 degrees) - - + + - -
degrees
sin (0) = 0
sin (30) = 0.5
sin (90) = 1
cos (0) = 1
cos (60) = 0.5
cos (90) = 0
tan (45) = 1
tan (135) = -1
sin (2x) = 2*sin(x)cos(x)
cos (2x) = cos^2 (x) - sin^2 (x) = 2*cos^2 (x) - 1 = 1 - s*sin^2 (x)
that's most of what I memorized for trig equalities. By the way...all of it helped me on exactly zero questions on the real DAT. The trig on the real QR is so basic you don't need to memorize crap...and I failed trig in high school, Twice.