Trigonometry Advanced Quiz 5
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Advanced Quiz 5
1. What is the dot product of vectors u = ⟨a, b⟩ and v = ⟨c, d⟩?
a
c
+
b
d
a
c
+
b
d
a
2
+
b
2
+
c
2
+
d
2
2. What is De Moivre’s Theorem?
[
r
(
cos
θ
+
i
sin
θ
)
]
n
=
r
n
[
cos
(
n
θ
)
+
i
sin
(
n
θ
)
]
r
=
a
2
+
b
2
tan
θ
=
sin
θ
cos
θ
3. What is the general equation for a line in polar coordinates?
r
=
a
b
+
c
cos
θ
y
=
m
x
+
b
r
2
=
a
2
+
b
2
4. What is the formula for the sum of two sine functions?
sin
A
+
sin
B
=
2
sin
[
A
+
B
2
]
cos
[
A
−
B
2
]
sin
A
+
sin
B
=
sin
(
A
+
B
)
+
sin
(
A
−
B
)
sin
A
+
sin
B
=
cos
(
A
+
B
)
−
cos
(
A
−
B
)
5. What is the product-to-sum identity for cosA cosB?
cos
A
cos
B
=
1
2
[
cos
(
A
+
B
)
+
cos
(
A
−
B
)
]
cos
A
cos
B
=
1
2
[
sin
(
A
+
B
)
+
sin
(
A
−
B
)
]
cos
A
cos
B
=
cos
(
A
+
B
)
+
cos
(
A
−
B
)
6. What is the period of the cotangent function?
π
2
π
π
2
7. What is the sum-to-product identity for cosA + cosB?
cos
A
+
cos
B
=
2
cos
[
A
+
B
2
]
cos
[
A
−
B
2
]
cos
A
+
cos
B
=
cos
(
A
+
B
)
+
cos
(
A
−
B
)
cos
A
+
cos
B
=
2
sin
[
A
+
B
2
]
sin
[
A
−
B
2
]
8. What is the sum-to-product identity for sinA − sinB?
sin
A
−
sin
B
=
2
cos
[
A
+
B
2
]
sin
[
A
−
B
2
]
sin
A
−
sin
B
=
sin
(
A
+
B
)
−
sin
(
A
−
B
)
sin
A
−
sin
B
=
cos
(
A
+
B
)
−
cos
(
A
−
B
)
9. In standard position, where is an angle of 270 degrees located on the unit circle?
On the positive x-axis
On the negative y-axis
On the positive y-axis
10. What is the quadrant of an angle whose terminal side is in the region where x is negative and y is negative?
Quadrant II
Quadrant I
Quadrant III
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