Solving Trigonometric Equations With A Calculator Problem Set

Name: ________________________ Class: ___________________ Date: __________
ID: A
Trigonometric Equations with a Calculator Problem Set
Short Answer
1. In the interval 0° ≤ A ≤ 360°, solve for all values of
A in the equation cos 2A = −3sinA − 1.
6. Find all values of x in the interval 0° ≤ x < 360°
that satisfy the equation 3cos 2x = cos x + 2.
Express your answers to the nearest degree. [The
use of the grid is optional.]
2. Solve the following equation algebraically for all
values of θ in the interval 0° ≤ θ ≤ 180°.
2sin θ − 1 = 0
3. Find, to the nearest degree, all values of θ in the
interval 0° < θ < 360° that satisfy the equation
3cos 2θ + sin θ − 1 = 0.
4. Find, to the nearest degree, all values of θ in the
interval 0° ≤ θ ≤ 180° that satisfy the equation
8cos 2 θ − 2cos θ − 1 = 0.
7. What value of x in the interval 0° ≤ x ≤ 180°
satisfies the equation 3 tanx + 1 = 0?
5. 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.]
1
ID: A
Trigonometric Equations with a Calculator Problem Set
Answer Section
SHORT ANSWER
1. ANS:
.
210°, 330°.
.
.
PTS: 4
REF: 060131b
KEY: double angle identities
2. ANS:
.
30, 150.
PTS: 2
KEY: basic
STA: A2.A.68
REF: 010523b
TOP: Trigonometric Equations
.
STA: A2.A.68
1
.
TOP: Trigonometric Equations
ID: A
3. ANS:
.
42, 138, 210, 330.
.
.
PTS: 4
REF: 060530b
KEY: double angle identities
4. ANS:
.
STA: A2.A.68
60, 104. Substitute x for cos θ.
TOP: Trigonometric Equations
. Substitute back cos θ for x.
.
PTS: 4
KEY: quadratics
.
REF: 010727b
.
STA: A2.A.68
2
.
TOP: Trigonometric Equations
.
ID: A
5. ANS:
.
90°, 221.81°, 318.19°.
.
PTS: 4
REF: 060829b
KEY: double angle identities
.
.
STA: A2.A.68
3
TOP: Trigonometric Equations
ID: A
6. ANS:
.
0°, 146°, 214°.
.
.
PTS: 6
KEY: grids
7. ANS:
150°
REF: 080833b
.
STA: A2.A.68
.
PTS: 2
KEY: basic
REF: 060319b
.
.
STA: A2.A.68
4
TOP: Trigonometric Equations
.
TOP: Trigonometric Equations