Trigonometry Advanced Quiz 2
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Advanced Quiz 2
1. What is the polar form of a complex number?
r
(
cos
θ
+
i
sin
θ
)
a
+
b
i
r
2
=
a
2
+
b
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 formula for the area of a triangle using two sides and the included angle?
Area
=
1
2
a
b
sin
C
Area
=
a
b
cos
C
Area
=
a
b
tan
C
4. What is the magnitude of a vector v = ⟨a, b⟩?
a
2
+
b
2
a
+
b
a
2
+
b
2
5. 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
6. 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
7. What is the half-angle identity for sine?
sin
2
(
x
2
)
=
1
-
cos
x
2
sin
2
(
x
2
)
=
1
+
cos
x
2
sin
2
(
x
2
)
=
1
-
sin
x
2
8. What is the half-angle identity for cosine?
cos
2
(
x
2
)
=
1
+
cos
x
2
cos
2
(
x
2
)
=
1
-
cos
x
2
cos
2
(
x
2
)
=
1
+
sin
x
2
9. What is the product-to-sum identity for sinA sinB?
sin
A
sin
B
=
1
2
[
cos
(
A
−
B
)
−
cos
(
A
+
B
)
]
sin
A
sin
B
=
1
2
[
sin
(
A
+
B
)
+
sin
(
A
−
B
)
]
sin
A
sin
B
=
sin
(
A
+
B
)
−
sin
(
A
−
B
)
10. What is the sum-to-product identity for sinA + sinB?
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
)
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