Question

Suppose that theta is an angle in standard position whose terminal side Intersects the unit circle at (-11/61, -60/61)

Find the exact values of tan theta, sec theta, and cos theta.

Answer 1

Answer:

The exact values of the tangent, secant and cosine of angle theta are, respectively:

$\cos \theta = -\frac{11}{61}$

$\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}$

$\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}$

Step-by-step explanation:

The components of the unit vector are $x = -\frac{11}{61}$ and $y = -\frac{60}{61}$. Since $r = 1$, then $x = \cos \theta$ and $y = \sin \theta$. By Trigonometry, tangent and secant can be calculated by the following expressions:

$\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}$

$\sec \theta = \frac{1}{\cos \theta} = \frac{1}{x}$

Now, the exact values of the tangent, secant and cosine of angle theta are, respectively:

$\cos \theta = -\frac{11}{61}$

$\tan \theta = \frac{-\frac{60}{61} }{-\frac{11}{61} } = \frac{60}{11}$

$\sec \theta = \frac{1}{-\frac{11}{61} } = -\frac{61}{11}$