Fill in the blank. Let θ be an angle in standard position, with (x, y) a point on the terminal side of θ and r = #sqrt(x^2 + y^2)≠ 0#?

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sec #theta#

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Answer 1 · 2017-04-06T13:54:51

#sectheta=sqrt(x^2+y^2)/x#

The secant of an angle is the inverse of the cosine of the angle -- that is, #sectheta=1/costheta#.

The cosine of an angle with your conditions is #x/r#, so the secant is #1/(x/r)=r/x#, which in this case is #sqrt(x^2+y^2)/x#