Q. Find the exact value of
sin 75°
A.
√2+√6
4
Q. Find the exact value of
cos 105°
A.
√2−√6
4
Q. Find the exact value of
2 sin 22.5° cos 22.5°
A.
√2
2
Q. Solve the equation
3 sin 𝑥 − 2 = 5 sin 𝑥 − 1, 0 ≤ 𝑥 < 2𝜋
A. 𝑥 =
7𝜋 11𝜋
6
,
A. (√8,
6
Q. Solve the equation
tan 3𝑥 = 1, 0 ≤ 𝑥 < 2𝜋
A. 𝑥 =
Q. Convert (−2, 2) from
rectangular coordinates to polar
coordinates
𝜋
,
,
4
,
12
,
12
,
4
Q. Solve the equation
2 cos2 𝑥 + cos 𝑥 − 1 = 0, 0 ≤ 𝑥 < 2𝜋
𝜋
5𝜋
3
3
A. 𝑥 = , 𝜋,
4
)
Q. Convert (2, − 2√3) from
rectangular coordinates to polar
coordinates
5𝜋 3𝜋 13𝜋 17𝜋 7𝜋
12 12
3𝜋
A. (4,
5𝜋
3
)
𝜋
Q. Convert (2, ) from polar
3
coordinates to rectangular
coordinates
𝜋
Q. Solve the equation
tan 𝑥 sin2 𝑥 = 3 tan 𝑥, 0 ≤ 𝑥 < 2𝜋
A. −√2 − 1
A. 𝑥 = 0, 𝜋
Q. Find the exact value of
𝜋
1 − 2 sin2
12
A.
Q. Solve the equation
cos 2𝑥 + 3 sin 𝑥 − 2 = 0, 0 ≤ 𝑥 < 2𝜋
6 2
6
Q. Solve the equation
1
sin 𝑥 cos 𝑥 = , 0 ≤ 𝑥 < 2𝜋
A. −√2 + 1
A. 𝑥 = ,
Q. Find the exact value of
𝜋
5𝜋
sin − sin
12
12
Q. Solve the equation
sin 𝑥 − cos 𝑥 = 1, 0 ≤ 𝑥 < 2𝜋
A. −
√2
2
Q. Find the exact value of
5𝜋
𝜋
sin
+ sin
12
12
A.
√6
2
2
𝜋 5𝜋
4
4
A. √29
Q. Find the product of
𝑧1 = 3(cos 5𝜋
+ 𝑖 sin 5𝜋
)
8
8
𝜋
𝜋
𝑧2 = 10(cos 16 + 𝑖 sin 16)
Q. Find the magnitude of
v = 2i − 3j
A. 30 (cos
A. √13
11𝜋
16
+ 𝑖 sin
11𝜋
16
)
Q. Find the product of
𝑧1 = 2(cos 𝜋6 + 𝑖 sin 𝜋6)
𝑧2 = 3(cos 𝜋4 + 𝑖 sin 𝜋4)
5𝜋
12
+ 𝑖 sin
5𝜋
12
)
Q. Find the quotient of
𝑧1 = 50(cos 80° + 𝑖 sin 80°)
𝑧2 = 10(cos 20° + 𝑖 sin 20°)
A. (√3, 1)
A. 5(cos 60° + 𝑖 sin 60°)
Q. Convert (− √3, −1) from
rectangular coordinates to polar
coordinates
Q. Find the quotient of
𝑧1 = 4(cos 𝜋5 + 𝑖 sin 𝜋5)
𝜋
𝜋
𝑧2 = 2(cos 10
+ 𝑖 sin 10
)
A. (2,
Q. Find the exact value of
7𝜋
tan
8
A. 28(cos 40° + 𝑖 sin 40°)
Q. Convert (2, ) from polar
6
coordinates to rectangular
coordinates
𝜋 𝜋 5𝜋
A. 𝑥 = , ,
√3
2
Q. Find the magnitude of
v = 5i − 2j
A. 6 (cos
A. (1, √3)
Q. Find the exact value of
tan 112.5°
Q. Find the product of
𝑧1 = 4(cos 15° + 𝑖 sin 15°)
𝑧2 = 7(cos 25° + 𝑖 sin 25°)
7𝜋
6
A. 2 (cos
)
Q. Convert (−2√3, 2) from
rectangular coordinates to polar
coordinates
𝜋
10
+ 𝑖 sin
𝜋
10
)
Q. Find the quotient of
𝑧1 = 12(cos 3𝜋
+ 𝑖 sin 3𝜋
)
4
4
𝜋
𝑧2 = 4(cos 4 + 𝑖 sin 𝜋4)
𝜋
𝜋
2
2
2
Q. Solve the equation
2 sin2 𝑥 − 3 cos 𝑥 = 0, 0 ≤ 𝑥 < 2𝜋
3
3
Q. If v starts at (−1, 6) and ends at
(7, −5), write v in terms of i and j.
A. v = 8i − 11j
Q. Given v = −3i + 7j and u = 2i −
5j find 3u + 4v
A. −6i + 13j
Q. Given v = −3i + 7j and w =
−i − 6j find 3w + 2v
A. −9i − 4j
Q. Convert (−8, ) from polar
3
coordinates to rectangular
coordinates
Q. Find (1 + 𝑖)5 using DeMoivre’s
Theorem. Write the answer in
rectangular form.
Q. Given v = −3i + 7j and w =
−i − 6j find 3v − 4w
A. (−4, −4√3)
A. −4 − 4𝑖
5𝜋
6
)
𝜋
𝜋
A. −5i + 45j
6
Q. Convert (−10, ) from polar
6
coordinates to rectangular
coordinates
Q. Find (√3 − 𝑖) using
DeMoivre’s Theorem. Write the
answer in rectangular form.
A. (−5√3, −5)
A. −64
𝜋 5𝜋
A. 𝑥 = ,
A. v = −8i + 11j
A. 3 (cos + 𝑖 sin )
A. (4,
𝜋
A. 𝑥 = , 𝜋
Q. If v starts at (2, −5) and ends at
(−6, 6), write v in terms of i and j.
Q. Given v = −3i + 7j and w =
−i − 6j find 4w − 3v
A. 5i − 45j