Let (-12,-5) be a point on the terminal side of Theta Find the exact values of cosTheta ,secTheta and cotTheta cosTheta = secTheta = cotTheta =

To find the exact values of $\cos\Theta$, $\sec\Theta$, and $\cot\Theta$ for a point $(-12,-5)$ on the terminal side of $\Theta$, we can use the definitions of trigonometric functions in terms of the coordinates of a point on the terminal side of an angle.<br /><br />Step 1: Find the radius (r) using the Pythagorean theorem:<br />$r = \sqrt{x^2 + y^2}$<br />$r = \sqrt{(-12)^2 + (-5)^2}$<br />$r = \sqrt{144 + 25}$<br />$r = \sqrt{169}$<br />$r = 13$<br /><br />Step 2: Find $\cos\Theta$:<br />$\cos\Theta = \frac{x}{r}$<br />$\cos\Theta = \frac{-12}{13}$<br /><br />Step 3: Find $\sec\Theta$:<br />$\sec\Theta = \frac{1}{\cos\Theta}$<br />$\sec\Theta = \frac{1}{-\frac{12}{13}}$<br />$\sec\Theta = -\frac{13}{12}$<br /><br />Step 4: Find $\cot\Theta$:<br />$\cot\Theta = \frac{x}{y}$<br />$\cot\Theta = \frac{-12}{-5}$<br />$\cot\Theta = \frac{12}{5}$<br /><br />Therefore, the exact values are:<br />$\cos\Theta = -\frac{12}{13}$<br />$\sec\Theta = -\frac{13}{12}$<br />$\cot\Theta = \frac{12}{5}$