Homework Supplement for 5.4 angle of inclination

Homework Supplement for 5.4
Graphed in the diagram is the linear equation
. The angle is the angle of inclination
for the line. Notice that this angle is defined by a
right triangle formed from its slope:
.
y
Δy
For example, if the slope of the line is
, then
the side opposite is 3 and the adjacent side is 5.
θ
Δx
To find the angle, we would just use the tangent
ratio:
.
1. Find the angle of inclination for the equation
β
y
α
At the left we have the graphs of two linear equations:
with an angle of inclination of and
with an angle of inclination of . What
we want to find is , the angle between the two lines.
Notice that we could just subtract our angles of
inclination to find :
.
θ
θα
x
θβ
Thus,
.
2. Use the difference formula for tangent to rewrite the
right side of
in terms of
and
.
x
Use the formula from Q2 to find the angle between each pair of equations.
3.
4.
5.