8.4
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Step-by-step solution
(a)
Consider the following parametric equation:
Curve of parametric equation is obtained using MAPLE as follows:
STEP 1: Start Maple and open a new document
STEP 2: Enter the following formula
Graph is obtained as follows:
(b)
8.3
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31Need to write the complex number in polar form with argument
and
between
.
From the definition of Polar form of complex numbers:
A complex number
where
and
and
is an argument of
Here in this case,
The
6.6
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25Consider the following triangle:
From the figure,
According the law of cosines,
Hence,
According to law of sines,
This implies that,
Therefore,
27We need to find the side x in the triangle ABC as shown below b
6.2
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11Need to use a calculator to evaluate the expression. Round the answer to five
decimal places.
Using graphing calculator:
After rounding the answer to five decimal places,
Using graphing calculator:
.
After rounding the answer to five dec
6.5
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Consider the triangle
for
, and
.
To solve this triangle, use sine rule as follows:
According to sine rule,
Put the values
, and
in this equation to get the value of
.
Let
then
In the triangle
,
.
Put
, and
From
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Consider the polar equation:
Graph of polar equation is obtained using MAPLE as follows:
STEP 1: Start Maple and open new document.
STEP 2: Enter the following equation:
Press enter to obtain the gra
6.3
5Need to find the reference angle for the below given angles.
The reference angle is the acute angle formed by the terminal side of the
angle
and the
-axis as shown in the below figure:
Since the terminal side of this angle is in Quadrant
, the refere
6.1
5Consider the angle
Recall that, relation between degrees and radians
To convert degrees to radians, multiply by
.
Consider the angle
Since
in degree measure, so multiply
So,
Therefore the radian measure of the angle
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by
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11Need to find the radian
6.4
5Need to find the exact value of each expression, if it is defined. Need to express
the answer in radians.
The angle in the interval
Hence the required value is
The angle in the interval
Hence the required value is
The angle in the interval
Hence the
8.1
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Need to find do the polar coordinates
Here the polar coordinates
Yes the polar coordinates
Thus the required polar coordinates
point.
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represent the same point
represent the same point
represent the same point
represent the same
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