Trigonometry Angles--Pi/15

cos(pi/(15))

=

1/8(sqrt(30+6sqrt(5))+sqrt(5)-1)

cos((2pi)/(15))

=

1/8(sqrt(30-6sqrt(5))+sqrt(5)+1)

cos((4pi)/(15))

=

1/8(sqrt(30+6sqrt(5))-sqrt(5)+1)

cos((7pi)/(15))

=

1/8(sqrt(30-6sqrt(5))-sqrt(5)-1)

cot(pi/(15))

=

sqrt(7+2sqrt(5)+2sqrt(15+6sqrt(5)))

cot((2pi)/(15))

=

sqrt(7-2sqrt(5)+2sqrt(15-6sqrt(5)))

cot((4pi)/(15))

=

sqrt(7+2sqrt(5)-2sqrt(15+6sqrt(5)))

cot((7pi)/(15))

=

sqrt(7-2sqrt(5)-2sqrt(15-6sqrt(5)))

csc(pi/(15))

=

sqrt(8+2sqrt(5)+2sqrt(15+6sqrt(5)))

csc((2pi)/(15))

=

sqrt(8-2sqrt(5)+2sqrt(15-6sqrt(5)))

csc((4pi)/(15))

=

sqrt(8+2sqrt(5)-2sqrt(15+6sqrt(5)))

csc((7pi)/(15))

=

sqrt(8-2sqrt(5)-2sqrt(15-6sqrt(5)))

sec(pi/(15))

=

+2-sqrt(5)+sqrt(15-6sqrt(5))

sec((2pi)/(15))

=

-2-sqrt(5)+sqrt(15+6sqrt(5))

sec((4pi)/(15))

=

-2+sqrt(5)+sqrt(15-6sqrt(5))

sec((7pi)/(15))

=

+2+sqrt(5)+sqrt(15+6sqrt(5))

sin(pi/(15))

=

1/4sqrt(7-sqrt(5)-sqrt(30-6sqrt(5)))

sin((2pi)/(15))

=

1/4sqrt(7+sqrt(5)-sqrt(30+6sqrt(5)))

sin((4pi)/(15))

=

1/4sqrt(7-sqrt(5)+sqrt(30-6sqrt(5)))

sin((7pi)/(15))

=

1/4sqrt(7+sqrt(5)+sqrt(30+6sqrt(5)))

tan(pi/(15))

=

sqrt(23-10sqrt(5)-2sqrt(255-114sqrt(5)))

tan((2pi)/(15))

=

sqrt(23+10sqrt(5)-2sqrt(255+114sqrt(5)))

tan((4pi)/(15))

=

sqrt(23-10sqrt(5)+2sqrt(255-114sqrt(5)))

tan((7pi)/(15))

=

sqrt(23+10sqrt(5)+2sqrt(255+114sqrt(5))).

sin(pi/(15))

=

sin(pi/6-pi/(10))

=

sin(pi/6)cos(pi/(10))-sin(pi/(10))cos(pi/6)

=

1/2sqrt(1/8(5+sqrt(5)))-(sqrt(3))/2&#183;&#183;1/4(sqrt(5)-1)

=

1/(16)(2sqrt(3)-2sqrt(15)+sqrt(40+8sqrt(5)))

cos(pi/(15))

=

cos(pi/6-pi/(10))

=

cos(pi/6)cos(pi/(10))+sin(pi/6)sin(pi/(10))

=

(sqrt(3))/2sqrt(1/8(5+sqrt(5)))+1/2&#183;1/4(sqrt(5)-1)

=

1/8(sqrt(30+6sqrt(5))+sqrt(5)-1).