
(a)
To find: The value of
(a)

Answer to Problem 33WE
The values are
Explanation of Solution
Given information:
Use the half angel formula for sine and cosine.
Calculation:
Half-angle formula for the sine:
Half-angle formula for cosine:
Thus,
Since
Therefore, by applying Half-angle formula for the sine, we get
Therefore, the value of
Calculate the value of
Since,
Therefore, by applying Half-angle formula for the cosine, we get
Therefore, the value of
(b)
To find: The value of
(b)

Answer to Problem 33WE
The value of
Explanation of Solution
Given information:
Use answers of (a)
Calculation:
From part (a) we have,
Since,
Thus,
Therefore, it is showed the value of
(c)
To Find: The value of
(c)

Answer to Problem 33WE
Proved the value of
Explanation of Solution
Calculation:
Show that
Half-angle formula for the tangent
Thus,
Since
Therefore, by applying Half-angle formula for the tangent, we get
Therefore, it is showed the value of
(d)
To show: Whether answers of (a) and (b) are equal.
(d)

Answer to Problem 33WE
The answers of (a) and (b) are equal.
Explanation of Solution
Calculation:
From part (a), we see that,
From part (c), we see that,
Thus, it is proved that the answers to parts (b) and (c) are equal.
Consider the identity,
Prove the given identity.
According to Pythagorean identity:
And Double-angle formula for the sine:
Consider left hand side,
Applying Pythagorean identity,
Now,
Since
Applying Double-angle formula for the sine we get,
Therefore, the value of (a) and (b) are equal
Chapter 13 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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