Trignonmetry
posted by Jaime on .
Please find the exact values:
Tan(3p/4)=
Sec(2p/3)=
Csc(7p/4)=
Cot(11p/6)=
p=pie

3pi/4 = 2pi 3pi/4 = + 5 pi/4
so you really want tan 5pi/4 which is pi/4 below the y axis
x = 1
y = 1
y/x = tangent = 1
sec 2 pi/3 = 1/cos 2 pi/3
that angle is between pi/2 and pi, second quadrant
pi  2 pi/3 = pi/3 above y axis
x = 1
y = +sqrt 3
sqrt(x^2+y^2) = hypotenuse = 2
so
cos(2pi/3) = 1/2
sec(2 pi/3)= 2
etc. draw the triangles 
You should be familiar with the trig ratios of the 306090º triangle as well as the 454590º triangle
pi/4 radians <> 45º
pi/3 radians <> 60º
pi/6 radians <> 30º
all your given angles are multiples of these.
I will do the last one
cot(11pi/6) = 1/tan(11pi/6)
11pi/6 is in the fourth quadrant, in the fourth quadrant the tangent is negative, so the cotangent is negative.
The angle is pi/6 away from the xaxis, so the 'angle in standard position' is pi/6
tan pi/6 = 1/√3, so cot pi/6 = √3
then cot(11pi/6) = √3
do the others the same way. 
What is sin of 660?
And
What is csc(2pi)/3?