math math please help?

Question

sin (9pi/4) using coterminal angle to find the exact value without a calculator.

(pi/4) * (9pi/4) = (8pi/4) + (pi/4) = 2pi + (pi/4) so sin (9pi/4)=sin 2pi +(pi/4) and =sin(pi/4) = 1

did I do this right???


how would I do sec 540 degrees??


please help and explain, thanks

Answer 1

9pi/4 = 2pi+pi/4
so sin (9pi/4) = sin(pi/4) = 1/2sqrt(2)
sec = 1/cos and 540º = 2*270* so
cos 540 = cos 2*270 = cos^2 270 -sin ^2 270= -1
so sec 540 =-1
also 540 =360 +180 so cos 540 = cos 180 =-1

Answer 2

9pi/4 -2pi = 9pi/4 -8pi/4 = pi/4
So 9pi/4 and pi/4 are coterminal
sin pi/4 = sqrt(2)/2 = .7071067812

sec (540) = sec (540-360) = sec (180) = -1

Answer 3

you did it well. I would say 9pi/4-2pi=pi/4 and sin(pi/4)=1

sec 540=sec (540-360)=sec(180)=1