# Finding Angle of Inclination With a Given Slope

1. Mar 28, 2016

### onemic

1. The problem statement, all variables and given/known data
Find the angle of inclination of a line when the slope, m, is equal to -1/2

2. Relevant equations
m = rise/run = tan(φ)

φ=angle of inclination

3. The attempt at a solution

I thought the answer would simply be using arctan on the slope, but my answer gives me -26.565051 degrees when the answer is supposed to be 153 degrees:

arctan(-1/2) = 26.565051

2. Mar 28, 2016

### Ssnow

yes, in fact $180°-26,6°=153,4°$ it is the same angle... (remember that the period of the tangent is $\pi$)

3. Mar 28, 2016

### onemic

Ahhh, thank you! I've been scratching my head at this for a few days now. I dont think the Calculus text Im using(Anton Calculus 6th ed.) ever talked about the period of the tangent being π. Or I somehow missed it.

4. Mar 28, 2016

### LCKurtz

Remember that the arctan function on a calculator gives answers in the principal value range, $(-\frac \pi 2,\frac \pi 2)$, but the angle of inclination of a line is between $0$ and $\pi$. That's why you need the second quadrant angle.