Transcript Solving Trig Equations

Solving Trig Equations
Starter C
Starter C Solutions
Starter D
Starter D Solutions
Starter A
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Solve these equations. 0° ≤ x ≤ 360°
‘Achieve’
1) Sin(x) = 0.82
2) Cos(x) = 0.49
3) Tan(x) = 0.14
4) Sin(x) = 0.38
Starter A Soln
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Solve these equations. 0° ≤ x ≤ 360°
y
1
1) Sin(x) = 0.82
0.5
90
180
270
180
360 x
S
A
T
C
S
A
T
C
S
A
T
C
S
A
T
C
0, 360
– 0.5
– 1
y
1
0.5
2) Cos(x) = 0.49
90
180
270
360 x
180
– 0.5
0, 360
– 1
y
2
1.5
1
0.5
– 0.5
90
180
270
360 x
3) Tan(x) = 0.14
180
– 1
0, 360
– 1.5
– 2
– 2.5
y
1
0.5
4) Sin(x) = 0.38
90
– 0.5
– 1
180
270
360 x
180
0, 360
Starter B
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Solve these equations
‘Achieve’
1) Cos(x) = -0.34
0° ≤ x ≤ 360°
2) Tan(x) = -2.4
0° ≤ x ≤ 360°
3) Sin(x) = 0.77
0 ≤ x ≤ 2π
4) Cos(x) = 0.14
0 ≤ x ≤ 2π
Starter B Solutions
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y
1
1) Cos(x) = -0.34
0.5
0° ≤ x ≤ 360°
180
90
180
270
360 x
S
A
T
C
S
A
T
C
S
A
T
C
S
A
T
C
0, 360
– 0.5
– 1
y
2
1.5
1
2) Tan(x) = -2.4
0.5
– 0.5
90
180
270
0° ≤ x ≤ 360°
180
360 x
– 1
– 1.5
0, 360
– 2
– 2.5
y
1
0.5
90
180
270
360 x
3) Sin(x) = 0.77
0 ≤ x ≤ 2π
– 0.5
π
0, 2π
– 1
y
1
0.5
90
– 0.5
– 1
180
270
360 x
4) Cos(x) = 0.14
0 ≤ x ≤ 2π
π
0, 2π
Starter C
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Solve these equations.
1) 4Sin(x) = 3.2
0° ≤ x ≤ 360°
2) Cos(x) + 3 = 3.19
0 ≤ x ≤ 2π
3) 0.5Tan(x) = 0.24
0 ≤ x ≤ 2π
4) 3Sin(x) + 1 = -1.8
0° ≤ x ≤ 360°
Starter C Solutions
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y
1
0.5
90
180
270
360 x
1) 4Sin(x) = 3.2
0° ≤ x ≤ 360°
2) Cos(x) + 3 = 3.19
0 ≤ x ≤ 2π
3) 0.5Tan(x) = 0.24
0 ≤ x ≤ 2π
180
– 0.5
S
A
T
C
0, 360
– 1
y
1
0.5
90
180
270
360 x
π
– 0.5
S
A
T
C
S
A
T
C
S
A
T
C
0, 2π
– 1
y
2
1.5
1
0.5
90
– 0.5
180
270
360 x
π
– 1
0, 2π
– 1.5
– 2
– 2.5
y
1
0.5
90
– 0.5
– 1
180
270
360 x
4) 3Sin(x) + 1 = -1.8
0° ≤ x ≤ 360°
180
0, 360
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Starter D
Sketch these graphs.
1) y = 2Sin(x) + 1
0° ≤ x ≤ 360°
3
2
1
– 1
– 2
2) y = Cos(x) + 3
0 ≤ x ≤ 2π
3) y = 0.5Tan(x)
0 ≤ x ≤ 2π
4) y = 3Sin(x) + 1
0° ≤ x ≤ 360°
y
90
180
270
360 x
Starter E
Home
Solve these equations. 0° ≤ x ≤ 360°
‘Achieve’
1) Cos x = 0.42
2) 4Cos x = 3.2
3) Tan x + 1 = 2.5
‘Merit’
4) Sin(x + 20) = 0.6
0 ≤ x ≤ 2π 5) Sin 2x = 0.3
For # 5 - 8
6) 4Cos x + 14 = 15
(Ist solution only)
7) Sin (x – 1) = -0.85
8) 2Tan x + 8 = 9.4
(Ist solution only)
Home
Starter E Solutions
Solve these equations. 0° ≤ x ≤ 360°
‘Achieve’
‘Merit’
1) Cos x = 0.42
Positive Cos so quadrant 1 & 4
x = 65.2° or 294.8°
360 – 65.2° = 294.8°
180
S
A
T
C
0, 360
2) 4Cos x = 3.2
Cos x = 0.8
x = 36.9° or 323.1°
3) Tan x + 1 = 2.5
Tan x = 1.5
x = 56.3° or 236.3°
4) Sin(x + 20) = 0.6
Let ‘A’ = (x + 20)
x = 16.9° or 106.9°
0 ≤ x ≤ 2π 5) Sin 2x = 0.3
Let ‘A’ = 2x x = 0.15 or 1.42 or 3.29 or 4.56
For # 5 - 8
4Cos x = 1
6) 4Cos x + 14 = 15
x = 1.32 or 4.97
st
(I solution only)
Cos x = 0.25
7) Sin (x + 1) = -0.85
x = 3.16 or 4.27
8) 2Tan x + 8 = 9.4
(Ist solution only)
x = 2.90 or 6.04