8-1 Angle of Inclination

Finding the angle of inclination is quite simple when applying either formulas:

m=tan (theta) or tan2A=B/A-C

Some things to keep in mind when performing these types of problems:

- Make sure to isolate the trig function

- Always have a calculator by side because when you take the inverse of tan you will need it.

Here's an example:

Find the angle of inclination of 2x+5y=13

(If you remember that m= -A/B(i.e. 2 is A and 5 is B)

-2/5= tan theta so when isolated it's theta =tan (inverse) -2/5

(Hint: Do not stop and think after you have plugged this into your calculator that you are finished; you still have to find out what quadrants the answer can be found in)

So, when plugged into calculator you get theta = 21 degrees 48 minutes 4 seconds

Now, this isn't the answer because the slope is negative and the answer can only be found negative in quadrants II and IV

so make the quadrant I angle negative and add 180 degrees to it so it can be converted to a quadrant II angle.

When done, you should get 158. 199 degrees

To convert the quadrant I angle to a quadrant IV angle you must make it negative and add 360 degrees to it

When done, you should get 338.199 degrees

Convert these answers to degrees minutes and seconds and you are finished

So the answers are as follows 158 degrees 11 minutes 56 seconds

338 degrees 11 minutes 56 seconds

~Sameer