Download PC12_LG11_Trig_Eqs2

PC 12 LG 11 Worksheet2 (Trig Equations)
1. Solve by graphing, if 0 ≤ x < 2π
7.
Solve the equation below over each of the
given domains. 2sin 2 x − sin x −1 = 0
a. Sin2x + Cos3x = 1.5
b. 3Sinx = x + 1
a. 0 ≤ x < 2π
c. x2Sinx = -x
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2.
b. π ≤ x < 2π
Find the exact value of A if 0 ≤ A < 2π
a. 2SinA + 1 = 0
b.
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3 + 2SinA = 0
c. 0 ≤ x <
c. 2TanA = 2
π
2
d. 4SinA + 2 = 2SinA + 1
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d.
π
3π
≤x<
2
2
e.
π
≤ x < 2π
2
3. Solve to 2 decimal places, if 0 ≤ x < 2π
a. 3Sinx + 2 = 0
b. 5Cosx – 4 = 0
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c. 4Tanx + 1 = 2Tanx + 5
4.
5.
Why do the equations of SinA = 2 and
CosA = -3 have no solutions and TanA = 4
have solutions?
Solve exactly using the square root property,
if 0 ≤ x < 2π
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a. 2Cos2x – 1 = 0
b. 4Sin2x – 3 = 0
c. 4Tan2x – 4 = 0
6.
Solve exactly , if 0 ≤ x < 2π.
extraneous roots.
a. (2Sinx + 1)(Sinx – 1) = 0
f. −π ≤ x < 0
8.
Solve each of the following equations
algebraically for x, 0 ≤ x < 2π. Give exact
values where possible (otherwise to 2 dec.
places). Also, solve over the set of real
numbers (give the general solution).
a. 2sin x tan x − tan x = 0
Watch for
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b. (2Cosx – 1)(Cosx + 2) = 0
c. (Tanx – 1)(Cosx + 4) = 0
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b. tan x − 2cos x tan x = 0
PC 12 LG 11 Worksheet2 (Trig Equations)
Answer Key
c. cos x tan x − 3tan x = 0
a. 3.84, 4.37
c. 0, 3.44, 6.12
d. 3cos x tan x − tan x = 0
2.
a.
b.
e. tan 2 x = tan x + 2
3.
a. 3.87, 5.55
c. 1.11, 4.25
b. 0.64, 5.64
4.
SinA and CosA have a range of -1 ≤ A ≤ 1 and the range
of TanA is all real numbers.
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1.
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5.
f. sec 2 x − 2sec x = 3
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9.
Use identities to solve each of the following
equations algebraically for x, 0 ≤ x < 2π.
Give exact values where possible (otherwise
to 2 dec. places). Also, solve over the set of
real numbers (give the general solution).
a. sin2x − sin x = 0
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e. 1− cos2 x = 3sin x − 2
e.
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7π! 11π! π!
,
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6
6
2
a.
0, π,
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b.
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c.
b.
d.
f.
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7π! 11π!
,
6
6
π! 7π!
,
2 6
−5π! −π!
,
6
6
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π 5π
,
(+2nπ, n ∈ I )
6 6
€ π 5π
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0, π, ,
(+2nπ, n ∈ I )
3 3
0,π (+2nπ, n ∈ I )
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0,π,0.94,5.34 (+2nπ, n ∈ I )
3π 7π
e. 1.11,4.25, ,
(+2nπ, n ∈ I )
4 4
f. π,1.23,5.05 (+2nπ, n ∈ I )
€9.
a.
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€ 11π! π!
7π!
,
,
6
6
2
c. No solution
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π 5π
b. 3 , 3
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a.
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d. sin x − cos2x = 0
7π! 11π! π!
,
,
6
6
2
π 5π
c. 4 , 4
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7.
b. cos x + sin2x = 0
c. cos x = cos2x
π 2π 4π 5π
b. 3 , 3 , 3 , 3
a.
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4π 5π
3 , 3
7π 11π
d. 6 , 6
π 3π 5π 7π
a. 4 , 4 , 4 , 4
π 3π 5π 7π
c. 4 , 4 , 4 , 4
6.
8.
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7π 11π
6 , 6
π 5π
c. 4 , 4
b. 0.54, 1.8
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d.
b.
c.
d.
e.
π 5π
,
(+2nπ, n ∈ I )
3 3
π 3π 7π 11π
, ,
,
(+2nπ, n ∈ I )
2 2 6 6
0, π,
0,
2π 4π
,
(+2nπ, n ∈ I)
3 3
3π π 5π
, ,
(+2nπ, n ∈ I )
2 6 6
π
(+2nπ, n ∈ I )
2