Dana H. answered 01/21/20
CalTech PhD and MIT Instructor Specializing in Calculus
I use the following "unforgettable chart" from my high school trig teacher ("Boston" Bob Connolly):
n 0 1 2 3 4 n is the column which numbers the angles in Q1
θ 0 π/6 π/4 π/3 π/2 θ is the angle in radians in Q1
sinθ=√n/2 0 1/2 √2/2 √3/2 1 √n/2 generates the exact values of sinθ
cosθ 1 √3/2 √2/2 1/2 0 cosθ is sinθ backwards (the complement)
tanθ 0 1/√3 1 √3 ∞ tanθ = sinθ/cosθ
The key is plugging in each column number n in sequence, noting for n=4 that √4/2 = 2/2 = 1.
Just remember the formula √n/2 and you can construct sinθ and cosθ whenever you forget them.
That gets you Quadrant 1 and you get sinθ and cosθ in the other quadrants by using the appropriate sign.