Trigonometry Angles--Pi/12

cos(pi/(12))

=

1/4(sqrt(6)+sqrt(2))

cos((5pi)/(12))

=

1/4(sqrt(6)-sqrt(2))

cot(pi/(12))

=

2+sqrt(3)

cot((5pi)/(12))

=

2-sqrt(3)

csc(pi/(12))

=

sqrt(6)+sqrt(2)

csc((5pi)/(12))

=

sqrt(6)-sqrt(2)

sec(pi/(12))

=

sqrt(6)-sqrt(2)

sec((5pi)/(12))

=

sqrt(6)+sqrt(2)

sin(pi/(12))

=

1/4(sqrt(6)-sqrt(2))

sin((5pi)/(12))

=

1/4(sqrt(6)+sqrt(2))

tan(pi/(12))

=

2-sqrt(3)

tan((5pi)/(12))

=

2+sqrt(3).

sin(pi/(12))

=

sin(pi/3-pi/4)

=

-sin(pi/4)cos(pi/3)+sin(pi/3)cos(pi/4)

=

-1/2sqrt(2)(1/2)+1/2sqrt(3)(1/2sqrt(2))

=

1/4(sqrt(6)-sqrt(2)).

cos(pi/(12))

=

cos(pi/3-pi/4)

=

cos(pi/4)cos(pi/3)-sin(pi/3)sin(pi/4)

=

1/2(1/2sqrt(2))+1/2sqrt(3)(-1/2sqrt(2))

=

1/4(sqrt(6)+sqrt(2)).