-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
cos(2pi/3) = -1/2
sec(2 pi/3)= -2
etc. draw the triangles
You should be familiar with the trig ratios of the 30-60-90º triangle as well as the 45-45-90º 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 x-axis, 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?
What is csc(-2pi)/3?
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