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