Download Precal A 2013-2014

Name ____________________
Precalculus, Period _________
Date:____________
Teacher:_________
REVIEW for the FINAL EXAMS
Precalculus A, First Semester
Answer/Solve the following questions/problems. Show work completely & neatly to receive full credit.
Part 1: Beginning Trig
1. Give 3 angles that are coterminal with 50o.
2. Convert to 195o to radian measure. Leave answer in terms of π.
3. Covert 7π/3 to degrees.
4. If sin x = 1/3 in quadrant II, find the other 5 trig values
5. If the terminal side of angle contains the point (-4, 4), find the 6 trig values.
Trig Functions
6.a) Find sec 
if cos =
2
3
7 Pre-AP) . Evaluate sec , if sin   
6.b)
7
and tan >0
10
Find tan 
if sin  =
6
7
8. Find the A, B, C, & D, then write an equation for each graph.
a.
b.
9. For each equation, give the Principal Axis (vertical shift), Amplitude, Period, Phase Shift, Max & Min, and
Range.
5
 2

(x  3)   3
a. y =  cos 
2
 3

(Vertical shift, D) =____, Amp. (A) = ____,
Per.=____,
Ph.Shft. (C) =____, Range: _______
Per.=____,
Ph.Shft. (C) =____, Range: _______
Per.=____,
Ph.Shft. (C) =____, Range: _______
5
 
b f ( x)  sin   x     6 .
4 
2
(Vertical shift, D) =____, Amp. (A) = ____,
 3

x  3
c. f ( x)  3  50 cos 
 4

(Vertical shift, D) =____, Amp. (A) = ____,
d.


f ( x)  3  50sin  4 x  
3

(Vertical shift, D) =____, Amp. (A) = ____,
e.
Per.=____,
Ph.Shft. (C) =____, Range: _______
Per.=____,
Ph.Shft. (C) =____, Range: _______
f ( x)  sin  3x 
(Vertical shift, D) =____, Amp. (A) = ____,
10) . Which of the following choices is the equation for the given graph:
A)
y= 5sin(x)
B)
y= –5cos(x)
C)
y= –5sin(x)
D)
y= 5 cos (x)
11). The diagram below shows
the curve y = p + k cos (ax)
Find the value of p and k.
Linear and Angular Velocity (Pre-AP)
12. The diameter of a merry-go-round is 10  ft. If it turns at 6 rpm, what is the linear velocity
a) in feet per minute
b) in mph on its outer edge?
13. The diameter of a motorbike’s wheels is 30 inches. Find the angular velocity in (revolutions per minute)
rpm, if the motorbike is traveling at 40 mph.
14. Find the radius of the circle from which a sector is cut off. The area of the sector is 36 in2, and its central angle is
10
9
15) Find a, b, & c.
16)
RIGHT Triangle Trigonometry
17)
18) Find the angle of elevation of a ramp that is 50 ft long and which rises to a maximum height
of 20 ft.
19) Pre-AP
Graphing Sinusoids Pre-AP
Graph one cycle of each.
20. Y = 5cos(4X)
21. Y = 6 + 4sin(2πX)
----------------------------------------------------------------------------------------------------------------------------- --
22. Graph y= -2sin(2(x-/4))+3. (Hint: Maybe you need to visualize this first? y = -2sin(2(x))+3
Simplifying Trig Expressions (answers must be in exact values)
cosq
____23) Identify the value of that makes the expression undefined.
1- sin 2 q
a. 90o
b. 180o
c. 270o
d. 360o
24) If cos θ = 0.891, what is sin 2 θ?
Trig Identities and Equations
17. Simplify: (sin x)(cot x)(sec x).
19. Simplify: csc x - (cos x)(cot x)
18.
(sec y  tan y )(sec y  tan y )
sec y
20. Simplify: sec x
sin x
–
sin x
cos x
21.Simplify: 1 – cos2x
1 – sin2x
22. Simplify: sin(2x)
sin x
23.
1
1

1  sin x 1  sin x
24. tan x(1  sin 2 x)
25.
sin(2 x)
cos 2 x
sin 2 x
28.
1  cos x
Solve the folloring trig equations in the domain [0, 2

27. 2cos x – √3 = 0,
32
2 tan x cos x  tan x  0
28. 3tan2 x = 1,
29. 1 – sin2θ = 2,
33. sin(2x) = sin x
30. cos 2x – cos x = 0
34. 2sin 2 x  3sin x  2
31.
4cos2 x  4cos x  1  0
38. If tan x = 1.3, then what does tan x + cot x equal to?
Law of Cosines, Law of Sines, SAS Area
39.
In a triangle with side lengths 10, 12, and 15, find the measure of the largest angle.
40. In triangle DEF, D = 60o, E = 15o, d = 17 cm. Find the length of side e.
41. In triangle PQR, p = 5, q = 12, and R = 40o. Find the length of side R.
42. In triangle ABC, A= 30o, b = 10, c = 15. Find the area.
43. Find the area of a triangle with side lengths 5, 7, and 9.
44. A farmer is estimating the surface area of his barn to find how much paint he needs to buy. Shown below is a
triangular part of the barn which will be painted red.
a. Find the area of the triangle.
28°
28°
6018
ft m
b). One quart of paint that costs $14.96 can cover about 85 ft2. How much will it cost to paint the triangle?
45.
VECTORS
46.. Given the points P(8, -2) and Q(-3, -5), find PQ and |PQ|.
47. Given vectors a = ‹ 2, 4 › and b = ‹ -1, 7 ›, find 3a – 2b.
48. Given vector a = ‹ -2, -8 › and vector b = ‹ 12, -4 › , find the magnitude of |a+b|
49. Find the unit vector for 7i + 2j.
50. Given a = ‹ -2, 5 › and b = ‹ -1, -3 ›, find the dot product a∙b.
51. Find the angle between vectors p = 4i – 3j and q = 2i + 5
Find the components of the following vectors:
Find the area of the shaded portion of the circle.
How many triangles can be possibly formed given the following
conditions:
1) A = 36o;
a = 2; b = 7
2) B = 30o; b = 3; c = 6
2) What is the standard measure of the angle determined by
the point (–2, 2).
3) Find the radius of a 110o arc that is 10 inches long.