The Inverse Sine, Cosine, And Tangent Functions Worksheet Template Page 4
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6Example: Find the exact value of the composite function. Notice that the inverse function is on the outside.
1
sin
sin
and
a)
The angle
is between
(as required by the definition in the sine box on the
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10
2
2
previous page). Thus, the answer is _______________.
5
5
5
1
cos
cos
b)
The angle
is not between 0 and . What quadrant is
in? ___________ So this
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3
3
angle actually lies in one of the allowable quadrants; we just need to rewrite it so that it is between 0 and . The
answer is to write its reference angle (remember that a reference angle is the shortest distance between the
1
cos
cos
given angle and the x-axis). _____________ Thus, we can re-write the problem as :
, which,
by definition, equals _________________.
4
4
1
tan
tan
and
c)
The angle
is not between
(as required by the definition in the tangent box
5
5
2
2
on the previous page). This angle is in Quadrant ________. In this quadrant, tangent is __________________.
In what other quadrant does tangent have this sign? ___________ Is that quadrant one of the ones that our
4
tan
tan
angle can be from? ________ So
=
. Then we can rewrite the problem as
5
1
tan
tan
, which, by definition, equals _______________.
2
2
2
1
tan
tan
and
d)
The angle
is not between
. In fact, the angle
is in Quadrant ______.
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3
2
2
3
In this quadrant, tangent is _____________________. In what allowable quadrant does tangent have that sign?
2
tan
______________ So
would be the same as tangent of what angle? __________________ Thus, we
3
1
tan
tan
can rewrite the problem as
, and then by definition, this equals ________________.
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