Question

If sin(x) = -3/5 with x in quadrant IV, find the sec(x)

Answer 1

there is a picture of an angle \(x\) with \(\sin(x)=\frac{3}{5}\) part of the familiar 3 - 4 - 5 right triangle, so we know the other side is 4
therefore \(\cos(x)=\frac{4}{5}\) and \(\sec(x)=\frac{5}{4}\)

Answer 2

now we can think about the quadrant. in quadrant IV cosine is positive, and therefore so is secant. so your answer is \(\sec(x)=\frac{5}{4}\)