mth181 unit circle by pi/12
addition of squares
(a²+b²)=a²+2ab+b²
subtraction of squares
(a²-b²)=a²-2ab+b²
cos(π)
-1
cos(2π/3)
-1/2
cos(4π/3)
-1/2
sin(11π/6)
-1/2
sin(7π/6)
-1/2
half angle identity cos(θ/2)
cos(θ/2) = ±√((1+cosθ)/2)
cos(π/4)
√2/2
cos(11π/6)
√3/2
cos(π/6)
√3/2
sin(2π/3)
√3/2
sin(π/3)
√3/2
cos(23π/12)
√6+√2/4
cos(π/12)
√6+√2/4
cos(19π/12)
√6-√2/4
cos(5π/12)
√6-√2/4
sin(11π/12)
√6-√2/4
sin(π/12)
√6-√2/4
sin(3π/2)
-1
cos(3π/4)
-√2/2
cos(5π/4)
-√2/2
cos(11π/12)
-√6-√2/4
sin(π)
0
cos(2π)
1
addition/subtraction formula for cos(a±b)
cos(a)sin(b)±sin(a)cos(b)
addition/subtraction formula for sin(a±b)
sin(a)cos(b)±cos(a)sin(b)
half angle formula sin(θ/2)
sin(θ/2) = ±√((1-cosθ)/2)
cos(7π/4)
√2/2
sin(3π/4)
√2/2
sin(π/4)
√2/2
sin(5π/12)
√6+√2/4
sin(7π/12)
√6+√2/4
sin(5π/4)
-√2/2
sin(7π/4)
-√2/2
cos(5π/6)
-√3/2
cos(7π/6)
-√3/2
sin(4π/3)
-√3/2
sin(5π/3)
-√3/2
cos(17π/12)
-√6+√2/4
cos(7π/12)
-√6+√2/4
sin(13π/12)
-√6+√2/4
sin(23π/12)
-√6+√2/4
cos(13π/12)
-√6-√2/4
sin(17π/12)
-√6-√2/4
sin(19π/12)
-√6-√2/4
cos(3π/2)
0
cos(π/2)
0
sin(2π)
0
sin(π/2)
1
cos(5π/3)
1/2
cos(π/3)
1/2
sin(5π/6)
1/2
sin(π/6)
1/2
