With out a calculator

sec(150°)  = 1/ cos (150° )  = 1 / [ -√3 / 2]  =    -2 / √3 

cos(300°) =  1/2

csc (-3pi / 4)  =  csc (-135°)  = csc(360° - 135°)  = csc ( 225° )  =

1 / sin (225°)  = 1 / [-1 / √2 ]  =  - √2

$sec(150°)$

$\frac{1}{cos(150°)}$

$\frac{1}{\frac{-\sqrt{3}}{2}}$

$1\times(-\frac{2}{\sqrt{3}})$

$-\frac{2}{\sqrt{3}}$

$-\frac{2\sqrt{3}}{3}$

$cos(300°)$

$\frac{1}{2}$

$csc(-\frac{3\pi}{4})$

$\frac{1}{sin(-\frac{3\pi}{4})}$

$\frac{1}{-\frac{\sqrt{2}}{2}}$

$1\times(-\frac{2}{\sqrt{2}})$

$-\frac{2}{\sqrt{2}}$

$-\frac{2\sqrt{2}}{2}$

$-\sqrt{2}$