Reference Angles

You may find this well worth watching :)

https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-definition-of-trig-functions-1

okay part a

a) sec(3pi/4)        reference angle: pi/4  and Value is -2/sqroot2

I have drawn a unit circle.  It is an excellent idea for you to completely understand the unit circle and its significance.  It makes much of trigonometry much easier. :)

A unit circle is a circle centre (0,0) and radius 1 unit.

I have drawn the 3pi/4 angle where it belongs.  If you drop a perpendicular from the ray down onto the x axis you will form the reference angle at at the origin. So the reference angle is  pi/4

NOW  sec is  1/cos 

$$\\cos (\pi/4) = cos 45^0 = \frac{1}{\sqrt2}=\frac{\sqrt2}{2}=\frac{\frac{\sqrt2}{2}}{1}=\frac{adj}{hyp}\\\\
$the hypotenuse is 1 because it is the radius of the unit circle$\\
$so the x value must be $\frac{\sqrt2}{2}$ but it is negative, you can see that the x is negative there!\\
now \\
sec\left\frac{\pi}{4}\right=\frac{hyp}{adj}=\frac{1}{x\;co-ordinate}=\frac{1}{-\frac{\sqrt2}{2}}=\frac{-2}{\sqrt2}$$