Chapter 4.2, Problem 74E

Solution

To identify: The which column gives cotangent values, which gives secant values, and which gives cosecant values without using a calculator, Below is a simplified trig table for angles between 30° and 40°.

  $\begin{array}{cccc}Angle& ?& ?& ?\\ 30°& 1.1574& 1.7321& 2.0000\\ 32°& 1.1792& 1.6003& 1.8871\\ 34°& 1.2062& 1.4826& 1.7883\\ 36°& 1.2361& 1.3764& 1.7013\\ 38°& 1.2690& 1.2799& 1.6243\\ 40°& 1.3054& 1.1918& 1.5557\end{array}$

Column 1 represents secant, column 2 represents cotangent and column 3 represents cosecant.

Given information:

The given table is shown below:

  $\begin{array}{cccc}Angle& ?& ?& ?\\ 30°& 1.1574& 1.7321& 2.0000\\ 32°& 1.1792& 1.6003& 1.8871\\ 34°& 1.2062& 1.4826& 1.7883\\ 36°& 1.2361& 1.3764& 1.7013\\ 38°& 1.2690& 1.2799& 1.6243\\ 40°& 1.3054& 1.1918& 1.5557\end{array}$

Explanation:

Consider the given information:

The column1 are secant values because secant values increases with the increase in angle.

The column2 are cotangent values because cotangent is $1.732$ at 30°.

The column3 are cosecant values because cosecant is 2 at 30°.

Thus, Column 1 represents secant, column 2 represents cotangent and column 3 represents cosecant.