Pre-Calculus
REVIEW: Unit 3 (ch 4)
Name _________________________________
s = r 
A= ½ r2
𝑣=
sin 𝐴
A = ½absinC
𝑎
=
sin 𝐵
𝑏
=
𝑠
𝜔=
𝑡
sin 𝐶
𝑐
𝜃
𝑡
v=r
c2 = a2 + b2 – 2abcosC
1. Rewrite –54° in radians as a multiple of π.
5π
5π
3π
B – 12
A 12
3π
C – 10
D 10
2. Tires are rotating at a rate of 32 revolutions per minute. Find the angular speed of the tires in radians per minute.
A 16π rad/min
B 32π rad/min
C 64π rad/min
D 72π rad/min
3. Each roller under a conveyor belt has a radius of 0.5 meter. The rollers turn at a rate of 30 revolutions per second.
What is the linear speed of the conveyor belt?
A 94.25 m/s
4. Let tan θ =
12
,
5
B 1.57 m/s
C 0.28 m/s
D 4.71 m/s
where sin θ > 0. Find the exact value of sin θ.
5
5
A 13
12
B 12
13
C 13
D 12
π
5. Which of the following is an equation of the tangent function with period 4 , phase shift π, and vertical shift 1?
𝜋
4
A y = tan (4𝑥 − ) + 1
B y = tan (4x – 4π) + 1
𝑥
D y = tan (4x + 4π) + 1
C y = tan (4 − 𝜋) + 1
6. ARCHITECTURE The angle of elevation from the tip of a building’s shadow to the top of the building is 70° and the
distance is 180 feet. Find the height of the building to the nearest foot.
A 62 ft
B 169 ft
C 66 ft
D 495 ft
4
3
7. Find the exact value of cos (tan−1 ).
3
4
A5
5
B5
5
C3
D4
C4
D–4
8. State the amplitude of y = –2 sin (4x + π) + 1.
A1
B2
9. Find arcsin (−
𝝅
A−𝟔
√3
)
2
𝜋
, if it exists.
𝜋
B –3
C
𝟐𝝅
𝟑
D does not exist
10. ROOF The front view of a roof is a triangle ABC with mA = 102°, mB = 23°, and c = 20 feet. Find a.
A 8.0 ft
B 16.7 ft
C 23.9 ft
D 50.1 ft
11. Which of the following is a vertical asymptote for the graph of y = tan x?
𝜋
Bx=π
Ax=2
C x = 3π
Dx=0
C 8.8
D 11.0
12. In △DEF, D = 52°, e = 9, and f = 14. Find d.
A 6.3
B 8.7
13. GEOMETRY Mr. Moran designated a triangular area in his study hall in the cafeteria for group work. The
dimensions of the triangle are 12 feet, 22 feet, and 30 feet. What is the area of the triangle?
A 33.7 ft 2
B 93.4 ft 2
C 113.1 ft 2
D 143.8 ft 2
14. In RST, r = 2.4 in., s = 8.2 in., and t = 10.1 in. Find mS.
A 15.1°
B 21.7°
C 28.9°
15. Find the exact value of all 6 trigonometric function for θ =
Sin=
−√𝟐
𝟐
√𝟐
Cos= 𝟐
Tan=-1
Sec=√𝟐
Csc=-√𝟐
Cot=-1
D 33.3°
7𝜋
.
4
16. A sector of a circular patio intercepts an arc that is 3.1 meters long and has a central angle of 180. Find the diameter
and area of the patio using s = r and A = ½ r2. Round answers to the nearest whole number.
3.1=r𝝅 so r=.987
𝟏
A=𝟐 (. 𝟗𝟖𝟕)𝟐 𝝅=1.55 so 2𝒎𝟐
17. Let (–4, 5) be a point on the terminal side of an angle θ in standard position. Find the exact value of cos θ and cot θ.
cos𝜽 =
−𝟒√𝟒𝟏
𝟒𝟏
cot𝜽 =
−𝟒
𝟓
18. Use the given information to determine how many triangles exist, if any.
a) a = 12, b = 17, mA = 39°
Two Triangles
1st ∆
m<B=63°
m<A=39°
m<C=78°
2nd ∆
m<B=117°
m<A=39°
m<C=24°
b) a = 9, b= 7, mA = 108°
One Triangle, obtuse
angle means either one
triangle or none
c) a = 10, b = 15, mA = 117°
No Triangles Exist
19. The side view of a skateboard ramp is a triangle ABC with mA = 42˚, mB = 68˚, and c = 15 feet. Find a to the
nearest tenth.
a=10.7
20. In △RST, mR = 59˚, s = 12 in., and t = 4 in. Find the area of △RST to the nearest square inch.
Area=21i𝒏𝟐
Type equation here.
21. Locate the vertical asymptotes of y = sec (x – π) + 3.
𝟑𝝅 𝟓𝝅
,
𝟐
𝟐
X=
22. Describe all transformations, then graph y = –cos(2x - 2) – 1
y=-cos2(x-𝜋) − 1
Original
(0,1)
𝜋
a / b shift
(0,-1)
𝜋
( ,0)
( ,0)
(𝜋, −1)
( ,1)
2
(
3𝜋
2
,0)
(2𝜋, 1)
4
𝜋
2
(
3𝜋
4
,0)
(𝜋, −1)
h / k shift
(𝜋, −2)
(
(
(
5𝜋
4
3𝜋
2
7𝜋
4
x
, -1)
, 0)
, -1)
(2𝜋 , -2)
23. If tan θ = – √3 and sin θ > 0, find θ and identify one positive and one negative angle that are coterminal with the
given angle. Give your answers in radians.
𝟐𝝅
𝟖𝝅
+2𝝅= 𝟑
𝟑
𝟐𝝅
−𝟒𝝅
-2𝝅= 𝟑
𝟑
24. Find the area of the quadrilateral. Throughout the problem, round side lengths to the nearest tenth, angle measures to
the nearest degree, and each area to the nearest square foot.
Total Area: 176f𝒕𝟐
15 ft
9 ft
114°
101°
12 ft
25. Starting from Simpson’s Road, proceed N32°W for 320 m, then turn S56°W for 280 m to the old oak tree, then turn
S22°E until Mulberry Lane is reached, and finally turn N68°E 329 m along Mulberry Lane back to the starting point.
Find the area of the land. Throughout the problem, round side lengths to the nearest tenth, angle measures to the nearest
degree, and each area to the nearest square foot.
Total Area: 87086𝒎𝟐
S
26. From the Southeast corner of the cemetery on Burnham Road, proceed S78°W for 250 m along the southern boundary
of the cemetery until a granite post is reached, then S15°E for 180 m to Allard Road, then N78°E along Allard Road for
201 m until it intersects Burnham Road, and finally N30°E along Burnham Road back to the starting point. Find the area
of the land. Throughout the problem, round side lengths to the nearest tenth, angle measures to the nearest degree, and
each area to the nearest square foot.
C
Total Area: 40632𝒎𝟐