Suppose that tan(t)=7/5 and that t is in the 3rd quadrant. Find the exact value of sec(t).

x and y are negative in the 3rd quadrant.....so....

tan (t) = y / x = -7/-5 = 7/5 ...and.....

sec(t) = r / x where r = sqrt (x^2 + y^2) = sqrt (5^2 + 7^2) =

sqrt (49 + 25) = sqrt (74)

So......

sec(t) = sqrt (74) / -5 = -sqrt(74) /5