Multiply by 13
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Rewrite to place the radical on one side before squaring the two sides of the equation.
4. Find the domain and range of
Solution:
Domain:
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Range:
Use the fact that
(see Figure 4)
==>
==>
and
(see Figure 5)
Substitute in (1)
Figure 4
Figure 5
We now equation the expression above to 1 and solve for x
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a)
False
Let x = 1
then
and
undefined
b)
False
The secant of a negative number less than minus one is negative.
c)
True
Because 3 is in the domain of cos and in the range of cos-1.
d)
False
Because 3 is not in the domain of cos-1.
e)
False
Because 4p / 3 is in the domain of tan but not in the range of tan-1 .

recall:
Remark:

The general rule for deciding on the possible values of x in a composite function of the form:

outside_function(inside_function(x))

is: x must be in the domain of inside_function and in the range of outside_function.
Multiply the inequality by 2.
Subtract p from all sides.
5. Solve the equation , where
Solution:
Thus,
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or
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or
6. Answer with true or false
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(see Figure 2)
the guys above.
They are used
to draw the
graphs.
Note:
The coordinates of the graphs are not scaled equally.
13
5
12
3
4
5
Figure 1
Figure 2
Thus,
Math 002-041
Solutions to Cal Problems 6.5 - 6.6
A. Farhat
1. Find the exact value of .
Solution:
Let
and
This substitution transforms the question to finding the value of .
5
==>
==>
(see Figure 1)
Thus,
3. Solve the equation .
Solution:
Take sine of both sides and evaluate .
Let
and
Thus, we need to find
(1)
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