Assume that \( \theta \) is an angle in standard position whose terminal side contains the point \( (15,-8) \). Find the exact values of the following functions. (Simplify your answer. Type an integer or a fraction.) sec \( \theta=\square \) (Simplify your answer. Type an integer or a fraction.) cot \( \theta=\square \) (Simplify your answer. Type an integer or a fraction.)

To find the values of \( \sec \theta \) and \( \cot \theta \) for the angle \( \theta \) whose terminal side contains the point \( (15, -8) \), we first need to determine the radius \( r \) using the coordinates of the point. The radius \( r \) is given by the formula: \[ r = \sqrt{x^2 + y^2} \] where \( x = 15 \) and \( y = -8 \). Calculating \( r \): \[ r = \sqrt{15^2 + (-8)^2} = \sqrt{225 + 64} = \sqrt{289} = 17 \] Next, we can find the values of the trigonometric functions. 1. **Finding \( \sec \theta \)**: The secant function is defined as: \[ \sec \theta = \frac{r}{x} \] Substituting the values we have: \[ \sec \theta = \frac{17}{15} \] 2. **Finding \( \cot \theta \)**: The cotangent function is defined as: \[ \cot \theta = \frac{x}{y} \] Substituting the values we have: \[ \cot \theta = \frac{15}{-8} = -\frac{15}{8} \] Thus, the exact values are: \[ \sec \theta = \frac{17}{15} \] \[ \cot \theta = -\frac{15}{8} \]