Chapter 5.2, Problem 51E

To determine

Find the quadrant in which the terminal determined by t lies.

Answer to Problem 51E

  $II\text{ Quadrant}$

Explanation of Solution

Given information:

  $\sin t>0,and,\cos t<0$

  $\sin t>0$ :

  $\sin t$ in only positive or greater than 0 in quadrant 1 and 2.

  $\cos t<0$ :

  $\cos t$ is only negative or lesser than 0 in quadrant 2 and 4.

So, as we can see that in only 2^nd quadrant $\sin t$ is positive $\left(\sin t>0\right)$ and $\cos t$ is negative $\left(\cos t<0\right)$

Therefore, the resultant quadrant is: $\boxed{II\text{ Quadrant}}$