Find the value sin(tan-1(5/12)
Answers
final answer:- 0. 384615
Draw a triangle in the plane with vertices
(
1
,
5
12
)
,
(
1
,
0
)
, and the origin. Then
arctan
(
5
12
)
is the angle between the positive x-axis and the ray beginning at the origin and passing through
(
1
,
5
12
)
. Therefore,
sin
(
arctan
(
5
12
)
)
is
5
12
√
1
2
+
(
5
12
)
2
.
5
12
√
1
2
+
(
5
12
)
2
Multiply the numerator by the reciprocal of the denominator.
5
12
⋅
1
√
1
2
+
(
5
12
)
2
Simplify the denominator.
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5
12
⋅
1
13
12
Multiply the numerator by the reciprocal of the denominator.
5
12
(
1
(
12
13
)
)
Multiply
12
13
by
1
.
5
12
⋅
12
13
Cancel the common factor of
12
.
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5
(
1
13
)
Combine
5
and
1
13
.
5
13
The result can be shown in multiple forms.
Exact Form:
5
13
Decimal Form:
0. 384615