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OPGAVEN |
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1. |
Los op in [0, 4π]:
4 + 3sin (2x - 1) = 5. Geef je antwoord in twee decimalen |
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2. |
Los op in [0, 2π]:
cos(x + 1) = sin(3x + 2). Geef je antwoord in twee decimalen |
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OPLOSSING |
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1. |
4 + 3sin (2x - 1) = 5
⇒
3sin(2x - 1) = 1
⇒
sin(2x - 1) = 1/3
⇒ 2x
- 1 = 0,34 + k2π)
∨ 2x - 1 =
π
- 0,34 =2,80 + k2π
⇒ 2x
= 1,34 + k2π)
∨ 2x = 3,80 + k2π
⇒ x
= 0,67 + kπ
∨ x = 1,90 + kπ
Dat geeft de oplossingen {0.67, 1.90 ,
3.81, 5.04 , 6.95, 8.18 , 10.09 11.32} |
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2. |
cos(x + 1) = sin(3x + 2)
⇒
sin(0,5π
-(x + 1)) = sin(3x +
2)
⇒
sin(0,5π
- x - 1) = sin(3x + 2)
⇒
0,5π
- x - 1 = 3x + 2 + k2π
∨ 0,5π
- x - 1 =
π
- (3x + 2) + k2π
⇒
-4x = 1,43 + k2π
∨ 2x
= 3,71 + k2π
⇒
x = 0,36 + k0,5π
∨ x
= 1,86 + kπ
Dat geeft de oplossingen {0.36, 1.86
, 1.93, 5.00 , 3.50, 5.07} |
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