Download ExamView - First Degree Trigonometric Equation Problem Set.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
First Degree Trigonometric Equations Problem Set
Short Answer
1. What are the values of θ in the interval
0° ≤ θ < 360° that satisfy the equation
tan θ − 3 = 0 ?
4. What value of x in the interval 0° ≤ x ≤ 180°
satisfies the equation 3 tanx + 1 = 0?
5. A solution set of the equation 5sin θ + 3 = 3
contains all multiples of
2. What is the solution set for 2cos θ − 1 = 0 in the
interval 0° ≤ θ < 360°?
6. Solve the following equation algebraically for all
values of θ in the interval 0° ≤ θ ≤ 180°.
2sin θ − 1 = 0
-
3. What is the solution set of the equation
− 2 sec x = 2 when 0° ≤ x < 360°?
1
Name: ________________________
ID: A
11. In the interval 90° < x < 270°, what is the solution
of the equation csc x = −2?
7. Find the number of degrees in the measure of the
smallest positive angle that satisfies the equation
2cos x + 1 = 0.
-
8. Find, to the nearest ten minutes or nearest tenth of
a degree, all values of x in the interval
0° ≤ x < 360° that satisfy the equation
6cos 2 x − 5sin x − 5 = 0.
-
9. Find, algebraically, the measure of the obtuse
angle, to the nearest degree, that satisfies the
equation 5csc θ = 8.
-
10. Find all values of θ in the interval 0° ≤ θ ≤ 360°
that satisfy the equation 3cos 2θ + 2sin θ + 1 = 0,
and round all answers to the nearest hundredth of a
degree. [Only an algebraic solution can receive
full credit.]
2
ID: A
First Degree Trigonometric Equations Problem Set
Answer Section
SHORT ANSWER
1. ANS:
60º, 240º
tan θ −
3 =0
tan θ =
.
.
3
θ = tan −1
3
θ = 60, 240
PTS: 2
KEY: basic
2. ANS:
{60°,300°}
REF: fall0903a2
STA: A2.A.68
TOP: Trigonometric Equations
STA: A2.A.68
TOP: Trigonometric Equations
2cos θ = 1
cos θ =
1
2
θ = cos −1
PTS: 2
KEY: basic
1
= 60, 300
2
REF: 061203a2
1
ID: A
3. ANS:
{135°,225°}
− 2 sec x = 2
sec x = −
2
2
cos x = −
2
2
x = 135,225
PTS: 2
REF: 011322a2
KEY: reciprocal functions
4. ANS:
150°
STA: A2.A.68
.
PTS: 2
KEY: basic
5. ANS:
180°
.
REF: 060319b
REF: 080610b
.
STA: A2.A.68
.
PTS: 2
KEY: basic
TOP: Trigonometric Equations
TOP: Trigonometric Equations
.
STA: A2.A.68
2
.
TOP: Trigonometric Equations
ID: A
6. ANS:
.
30, 150.
PTS: 2
KEY: basic
7. ANS:
120
.
STA: A2.A.68
TOP: Trigonometric Equations
PTS: 2
REF: 069613siii
KEY: basic
8. ANS:
9º40’, 170º20’, 270º or 9.6º, 170.4º, 270º
STA: A2.A.68
TOP: Trigonometric Equations
PTS: 10
REF: 060239siii
KEY: pythagorean identities
9. ANS:
5csc θ = 8
STA: A2.A.68
TOP: Trigonometric Equations
STA: A2.A.68
TOP: Trigonometric Equations
csc θ =
8
5
sin θ =
5
8
REF: 010523b
.
θ ≈ 141
PTS: 2
REF: 061332a2
KEY: reciprocal functions
3
ID: A
10. ANS:
.
90°, 221.81°, 318.19°.
.
PTS: 4
REF: 060829b
KEY: double angle identities
11. ANS:
210º
PTS: 2
REF: 080130siii
KEY: reciprocal functions
.
.
STA: A2.A.68
TOP: Trigonometric Equations
STA: A2.A.68
TOP: Trigonometric Equations
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