Q. 88 - Precalculus Enhanced with Graphing Utilities

Question

Find the exact value of:$Tan 40°+Tan 140°$

Step-by-Step Solution

Answer

The value of $Tan 40°+Tan 140°=0$

Step 1. Given information

The given value is $Tan 40°+Tan 140°$

Step 2. Sketch the angle of 40 °

Sketch the angle of $40°$

Step 3. Sketch the angle of 140 °

The sketch of $140°$

Step 4. Finding the value of T a n   40 ° + T a n   140 °

The reference angle for $\theta$ is the acute angle formed by the terminal side of $\theta$ and the x- axis.We note that for the angle $40°$the angle formed with the x-axis is $40°$

thus,the reference angle $40° and 140° is 40°$

we note that the angle $40°$ lies in quadrant  I where the values of the tangent function is positive and $140°$ lies is in quadrant II,Where the values of the tangent function is negative.

Replace $\tan 140°$ with $-\tan 40°$in the given expression

$$\begin{gathered} \tan 40°+\tan 140°=\tan 40°-\tan 40° \\ = 0 \end{gathered}$$

Therefore,the given expression is evaluates 0