Since the sine is negative and the tangent is positive, the angle is in quadrant III
from sin theta = -4/9, r = 9 and y = -4
x^2 + y^2 = r^2
x^2 + 16 = 81
x = -sqrt(65) , in III the x is negativ
Then cos theta = -sqrt(65)/9
sec theta = -9/sqrt(65)
or -9sqrt(65)/65
Find the exact value of indicated trignometric function of theta.
Sin= -4/9 , tan theta>0 find sec
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