; Special angles, such as 17/6 pi radians
COS (17/6 pi)

; Use DEG to enter angles in degrees
SIN (-30 DEG)

; A hidden opportunity for sin^2 + cos^2 --> 1
(SIN x)^3 + SIN x + (COS x)^2 SIN x

; Using different rules in different places
(1 - (COS x)^2)^4 (1 - (SIN x)^2)^3 ((SIN x)^2 + (COS x)^2)^5

; Judicious extraction of phase angles
SIN (pi / 4 + a) - SIN (0.25 (pi - 4 a))
; Judicious extraction of phase angles
SIN (1.5 pi/2+x) / COS (pi+x) + COS ((3pi-2x)/2) / SIN (pi/2+x)
; Judicious extraction of phase angles
SIN (pi - a) / TAN (pi + a) * COT ((pi - 2 a)/2) / TAN (pi / 2 + a) * SIN (1.5 * pi + a) / SIN (- a)

; Judicious use of multiple-angle expansion
SIN (6 x) / SIN (3 x)

; Judicious use of half-angle transformations
1 + TAN a * TAN (a/2)
; Judicious use of half-angle transformations
(COS (a/2) + SIN (a/2))^2
; Judicious use of half-angle transformations
TAN (0.5 t) * (SIN ((pi - t) / 4))^2 * (SIN (pi/4 + t/4))^2

; Simultaneous half and multiple angles
CSC (2x) (2 (COS (x/2))^2 - 1)

; Cancellation of trig gcds
(1 + SIN a) * (1 + SEC a) / ((1 + COS a) * (1 + CSC a))
; Cancellation of trig gcds
(TAN a)^2 / (1 + (TAN a)^2) * (1 + (COT a)^2) / (COT a)^2

; Principal arctangent of a special ratio
ATAN (2 + SQRT 3)
; ATAN (y, x) is the angle of the point (x,y)
ATAN (-1, -1)
; Principal arcsine of a special ratio
ASIN (-1/2)
; Principal arccosine of a special ratio
ACOS (- 1 / SQRT 2)
; Judicious transformation of ASIN to ATAN
ASIN (x/SQRT(x^2 + 1))
; Judicious transformation of ATAN to ASIN
ATAN (x/SQRT(1-x^2))
; Exploitation of reciprocal arguments
ATAN (x/2 + 3) + ATAN (2/(x + 6))
; Composition of inverse functions
TAN ATAN x
; There is also an arcsecant function
ASEC (1/x)
; There is also an arccosecant function
CSC ACSC x
; There is also an arccotangent function
ACOT t + ATAN t
