Chapter 11.4, Problem 43STP

To determine

To find: The correct option.

Answer to Problem 43STP

The correct option is $C$ .

Explanation of Solution

Given:

The value of $\cos \theta =\frac{-12}{13}$ and $\pi <\theta <\frac{3\pi }{2}$ .

Calculation:

Consider the formula for cosine is,

  $\cos \theta =\frac{\text{adjacent}\text{side}}{\text{hypotenuse}}$

Then,

  $\cos \theta =-\frac{\text{12}}{\text{13}}$

Then,

  $\begin{array}{l}A{C}^2=B{C}^2-A{B}^2\\ A{C}^2={13}^2-{12}^2\\ A{C}^2=169-144\\ AC=5\end{array}$

Then, the tangent function is,

  $\begin{array}{c}\tan \theta =\frac{\text{opposite}\text{side}}{\text{adjacent}\text{side}}\\ =\frac{5}{12}\end{array}$

Thus, the correct option is $C$ .