Need help on trig problems?

Question

I know the answer to these problems but I DUNNO how to do them

Use the given function values and trig idenities (including cofunction idenities,)to find the indicated trig functions

1. sin 60 degrees= radical 3 /2, cos 60 degrees = 1/2

a) tan 60 deg
b) sin 30 deg

Evaluate the trig function using its period as an aid

1. sin 5 pie

Use the value of thr trig function to evaluate the indcated functions

1. sin t = 1/3

a) sin(-t)
b) csc (-t)

ONE MORE THING

this applies to evaluting the trig function usint its period as an aid

(A) cos (-15 pi /2 ).

I dunno why it is cos pi/2. Please explain. LIke how do u simplify

Answer 1

okay...sin(60 degrees) = Sqrt[3]/2 and cos(60 degrees) = 1/2

a) tan(60 deg) = sin(60deg) / cos(60deg) = (Sqrt[3] / 2) / (1/2) = Sqrt[3]

b) sin(30 deg) = cos(60 deg) = 1/2

period of sin is 2*pi
but you know that sin(n*pi + x) = sin(x) if n is even, or -sin(x) if n is odd...

sin(0) = 0
so sin(5*pi) = -sin(0) = 0

a) sin(-t) = -sin(t) = -1/3
b) csc(-t) = 1/sin(-t) = -1/sin(t) = -3

Answer 2

tan60 =sin60/cos60 = rad(3)/2* 2 = rad(3)
sin(30) = cos(60) = 1/2

sin(5pi) = sin(5pi-4pi) = sin (pi) = 0
The above hax no period. It is not a function.

sin(-t) = -sin(t) = -1/3
csc(t) = 1 /sint (t) = 3 so csc(-t) = -3