# Math Help - Inclination Question

1. ## Inclination Question

I have a problem in the book asking for inclination with a given slope. I'm told to use formula m = tan(inclination) as long as (0deg < or = Incl < 180deg)

Slope: -6.691

I use tan^-1(-6.691) and get -81.4 but the book says it's 98.5

2. Since the problem said "0deg < or = Incl < 180deg", -81.4 couldn't possibly be the correct answer, could it?

Hint: the tangent function is periodic with period 180 degrees.

3. ## True

True, it has to be positive. I've tried many different things, like subtracting the angle from 180 first. I'm stuck.

4. Did you get 180-81.4= 98.6 rather than 98.5? It's round off error. The "principal value" of $tan^{-1}(-6.691)$ is -81.4998 to 4 significant figures which rounds off to -81.5, not -81.6.

5. ## Now i see

I now see that you're subtracting the angle from 180 afterwards. But really it's addition, since -81.4 is negative. So, if the slope is negative, the angle will be negative. Add it to 180 to get the inclination. Is this correct?

6. Yes, -81.5+ 180= 180- 81.5. "subtract 81.5" is exactly the same thing as "add -81.5".