# 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?

## sec $\theta$

Apr 6, 2017

#### Answer:

$\sec \theta = \frac{\sqrt{{x}^{2} + {y}^{2}}}{x}$

#### Explanation:

The secant of an angle is the inverse of the cosine of the angle -- that is, $\sec \theta = \frac{1}{\cos} \theta$.

The cosine of an angle with your conditions is $\frac{x}{r}$, so the secant is $\frac{1}{\frac{x}{r}} = \frac{r}{x}$, which in this case is $\frac{\sqrt{{x}^{2} + {y}^{2}}}{x}$