math please help!!!?

Question

using the reference angle to find the exact value of each expression . . . without calculator

a) csc (7pi)/4, I said it's coterminal with (pi/4) so csc (7pi)/4 = csc (-2pi +(pi/4)) so csc = (pi/4) = sq root 2

did I do this right??

and how would i do this one??

b) cos (2pi) / 3


and c) sec (11pi)/4

sorry my book does a crappy job explaining this so I'm just having a hard time, if you could please help me, I would appreciate it! THANKS

Answer 1

There's an easier way to do that.

csc(x)=1/sin(x)

since sin(7pi/4) is -root(2)/2
just take 1/-root(2)/2
2/-root(2)=-root(2)

cos(pi/3)=1/2
2pi/3 would just make it negative

11pi/4 is the same as 3pi/4
cos(3pi/4)=-root(2)/2
1/-root(2)/2=-root(2)

Answer 2

Yes, the way to do this is correct except, you have to know which quad the angle is in and for 7pi/4, it is in quad 4, so sin and csc are negative.

I like to do it in degrees
2pi/3 = 120 cos 120 = cos 60 = rt(3)2
cos in quad 2 is also negative = -rt(3)/2

11pi/4 = 495
sec 495 = sec 135 = sec 45
in quad 2, sec is negative = -rt(2)

Answer 3

omg I wish knew..I hate math..but I hope someone helps you!