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Precalculus Examples
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Precalculus
Find the Direction Angle of the Vector 3i-4j
3
i
−
4
j
3
i
-
4
j
Step 1
Apply the direction
angle
formula
θ
=
arctan
(
b
a
)
θ
=
arctan
(
b
a
)
where
a
=
3
a
=
3
and
b
=
−
4
b
=
-
4
.
θ
=
arctan
(
−
4
3
)
θ
=
arctan
(
-
4
3
)
Step 2
Solve for
θ
θ
.
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Step 2.1
Remove parentheses.
θ
=
arctan
(
−
4
3
)
θ
=
arctan
(
-
4
3
)
Step 2.2
Evaluate
arctan
(
−
4
3
)
arctan
(
-
4
3
)
.
θ
=
−
0.92729521
θ
=
-
0.92729521
θ
=
−
0.92729521
θ
=
-
0.92729521
3
i
−
4
j
3
i
-
4
j
(
(
)
)
|
|
[
[
]
]
√
√
≥
≥
7
7
8
8
9
9
≤
≤
°
°
θ
θ
4
4
5
5
6
6
/
/
^
^
×
×
>
>
π
π
1
1
2
2
3
3
-
-
+
+
÷
÷
<
<
∞
∞
,
,
0
0
.
.
%
%
=
=
⎡
⎢
⎣
x
2
1
2
√
π
∫
x
d
x
⎤
⎥
⎦
[
x
2
1
2
π
∫
x
d
x
]
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