Download Name:_______________________________________________________ Date:__________ Period:_______ Trig Equations Test 1: Review Sheet

Name:_______________________________________________________ Date:__________ Period:_______
Trig Equations Test 1: Review Sheet
Algebra 2 HONORS
Trig Equations Test 1: Review Sheet
Complete all work on a separate sheet of paper.
Angle Sum & Difference:
Find the exact value of the following:
1.)
2.)
3.)
4.)
5.)
6.)
7.) If
is the value of
and
and a is in Quadrant III and b is in Quadrant I, what
?
8.) Evaluate the expression
given that
and
, with y in Quadrant III.
9.) If
value of
and
.
and both a and b are positive acute angles, find the
10.) If A and B are positive acute angles,
of
?
11.) If
12.) If
and
, with x in Quadrant II,
, and
, what is the value of
, where x is in Quadrant I, find the value of
13.) The expression
is equivalent to
(1) sinx
(2) –sinx
(3) cosx
14.) The expression
(1)
(2)
15.) The expression
(1) cosA
(2) –cosA
(4) –cosx
is equivalent to
(3)
(4)
is equivalent to
(3) sinA
(4) –sinA
, what is the value
?
.
Double Angle:
16.) If
, what is the value of
17.) If
is a positive acute angle such that
?
, what is the value of
?
18.) If
, what is
?
19.) If
, and <A lies in Quadrant IV, find the value of
20.)
and <A is in Quadrant I. Find, in simplest form, the value of
.
.
21.) The expression
(1) sin60
(2) cos60
has the same value as
(3) cos15
(4) sin15
22.) The expression
(1) sin20
(2) sin80
has the same value as
(3) cos80
(4) cos20
23.) The expression
(1)
(2)
has the same value as
(3)
(4)
Half Angle:
24.) If x is a positive acute angle and
25.) If
26.) If
27.) If
, what is the value of
, what is the positive value of
?
, and x is an angle in Quadrant I, find
, find the positive value of
?
.
.
Linear Trig Equations:
Solve for all values of , to the nearest degree, in the interval 0° ≤ < 360°.
28.) 6(tan  + 2) = 6
29.) 6sin  – 3 3 = 0
30.) 5sec  + 4 = 3sec 
31.) 3 cos θ = cos θ – 1
32.) -2 sin θ –
2 =0
34.) 3(sin θ – 1) = 0
35.) cot θ + 2 = 2 cot θ + 3
33.) 3 cos θ + 5 = 0
and
Quadratic Trig Equations:
Solve for all values of , to the nearest degree, in the interval 0 ≤
36.) cos2  + 7cos  – 8 = 0
37.) tan2  + tan  = 12
38.) 2sin2  + 20 = 22sin 
39.) sin  cos  + cos  = 0
40.) 2sin2  + 4sin  = 0
41.) cot2  = 7cot  – 10
42.) csc2  – 18 = 3csc 
43.) cos2θ – cos θ = 0
44.) sin2θ + 3 sin θ + 2 = 0
45.) cos2θ – 2 cos θ = 3
<2 .
46.) sec2θ = sec θ + 2
Case II: Solve for all values of , to the nearest degree, in the interval 0° ≤
47.) 2tan2  - 3tan  – 5 = 0
48.) 12cos2  – 3 = 5cos 
49.) 5sin2  + 26sin  + 5 = 0
50.) 8tan2  = 22tan  – 15
51.) 3sec2  – 11sec  = 4
52.) 10csc2  + 21csc  + 8 = 0
Quadratic Formula:
Solve for all values of , to the nearest degree, in the interval 0° ≤
53.) 4sin2  + 3sin  – 7 = 0
54.) tan2  + 11 = 7tan 
55.) 2cos2  = 5cos  + 1
56.) 3sec2  + 9sec  = 5
< 360°.
< 360°.
Review Questions:
57.) Determine the solution set for the following system of equations:
58.) Determine the nature of the roots of the equation
.
59.) The discriminant of a quadratic equation is 24. Describe the nature of the roots.
60.) For which positive value of m will the equation
that are real, equal, and rational?
(1) 12
(2) 9
(3) 3
(4) 4
have roots
61.) Find all value of k such that the equation
has imaginary roots.
62.) Factor the expression completely
.
63.) Factor completely:
64.) Find the solution set to the equation
.
65.) What is the solution set to the equation
?
66.) What is the solution set for the equation
?
67.) Rationalize:
68.) What is the product of
and its conjugate?
69.) Find the product of
and its conjugate.
70.) Sketch an angle of 240o in standard position. Then find the exact value of
sin240o.
71.) What is the solution set to the equation
72.) Find the roots of the equation
?
.
73.) The probability that Peter will get a 100 on his math test is 72%. To the nearest
thousandth, what is the probability that Peter will get a 100 on at least 3 out of the
next 5 math tests?
74.) The probability that it will snow on any given day is 12%. To the nearest tenth
of a percent, what is the probability that it will snow at most 2 out of 6 days?
75.) How many different 8 different letter arrangements can be made by using the
letters in “STANDARD”?
Answer Key:
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
9.)
10.)
11.)
12.)
13.) (2)
14.) (4)
15.) (4)
16.)
17.)
18.)
19.)
20.)
21.) (2)
22.) (3)
23.) (3)
24.)
25.)
26.)
28.) {135°,315°}
29.) {60°,120°}
30.) {120°,240°}
31.) {120°,240°}
32.) {225°,315°}
33.) No solution
34.) {90°}
35.) {135°,315°}
36.) {0}
37.)
38.)
39.)
40.)
41.)
42.)
43.)
44.)
45.)
46.)
47.) {68°,135°,248°,315°}
48.) {41°,109°,251°,319°}
49.) {192°,348°}
50.) {51°,56°,231°,236°}
51.) {76°,284°}
52.) {219°,321°}
53.) {90°}
54.) {67°,78°,247°,258°}
;
27.)
55.) {101°,259°}
56.) {107°,253°}
57.) (0,-6) & (4,6)
58.) imaginary
59.) real, irrational, unequal 60.) (1)
61.)
62.)
63.)
64.)
65.)
66.)
67.)
68.) 117
69.)
70.)
71.)
72.)
73.) 0.862
74.) 97.4%
75.) 10080