If the "terminal side" crosses the unit circle at point (x, y) then $\displaystyle cos(\theta)= x$, $\displaystyle sin(\theta)= y$. Of course, $\displaystyle tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$, $\displaystyle cot(\theta)= \frac{cos(\theta)}{sin(\theta)}$, $\displaystyle sec(\theta)= \frac{1}{cos(\theta)}$, and [tex]csc(\theta)= \frac{1}{sin(\theta)}[tex].
"All values of $\displaystyle \theta$ so the $\displaystyle cos(\theta)= -\frac{\sqrt{2}}{2}$." Since cosine is the x coordinate on the unit circle, where does the vertical line $\displaystyle x= -\frac{\sqrt{2}}{2}$ cross the unit circle, $\displaystyle x^2+ y^2= 1$?
Surely your text has a definition of "geometric sequence"?
Problem 8 simply asks you to calculate $\displaystyle (-1)^n(2n+ 9)$ for n= 1, 2, 3, 4, and 5.