Let a, whose coordinates are (–4, 3), be a point on the terminal side of angle t. find the exact value of sin (t) and sec (t).

When we plot the point a in the second quadrant we drop a vertical line down to the x-axis and a horizontal line to the y-axis. This forms a triangle with sides 3, 4, 5. We call x the angle between the x-axis and the line from the origin to the point (-4,3).

Recall that in quadrant two sin x and  csc x are positive. All others are negative.

sin x = (opp)/(hyp) = 3/5

sec x = 1/cos x = 1 / (4/5) = 5/4 but the sec function is negative in quadrant two so the answer we are looking for is -5/4