`m = -1` find the inclination 'theta' (in radians and degrees) of the line with slope m.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The given slope is `m = -1` .

Take note that if the slope of the line is given, to determine the angle of inclination, apply the formula:

`tan theta = m`

where `theta` is the angle measured counterclockwise from the positive x-axis going to the right of the...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

 

The given slope is `m = -1` .

Take note that if the slope of the line is given, to determine the angle of inclination, apply the formula:

`tan theta = m`

where `theta` is the angle measured counterclockwise from the positive x-axis going to the right of the line. And its range of values is from 0 to 180 degree only `(0^o lt= theta lt=180^o)` .

Plugging in the value of m, the formula becomes:

`tan theta = -1`

Then, take the inverse of tangent to isolate theta.

`theta =tan ^(-1)`

`theta = -pi/4 rad =-45^o`

Take note that when the computed value is negative, to get value of angle of inclination in the interval `0^o lt= thetalt=180^o` ,  add 180 degree (pi rad).

`theta = -pi/4 + pi = (3pi)/4` rad

`theta = -45^o + 180^o = 135^o`

Therefore, in radians, the angle of inclination is `(3pi)/4` rad. And in degree, the angle of inclination is `135^o` .

 

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)
Approved by eNotes Editorial Team