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| 1. | t
= 3/4π
geeft x = cos(3/4π)sin(3/2π) = -1/2√2 • -1 = 1/2√2 y = cos(3/4π) = -1/2√2 |
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| x ' = -sint •
sin(2t) + cos(t) • 2cos(2t) dus
x'(3/4π)
= -1/2√2
• -1 + -1/2√2
• 2 • 0 = 1/2√2
y '= -sint dus y '(3/4π) = -1/2√2 |
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| ze zijn inderdaad gelijk. | |||||
| 2. | a | y
= 0 sin(2t) - sin(t) = 0 sin(2t) = sin(t) 2t = t + k2π ∨ 2t = π - t + k2π t = 0 + k2π ∨ 3t = π + k2π t = 0 ∨ t = 2π ∨ t = 1/3π + k2/3π t = 0 ∨ t = 2π ∨ t = 1/3π ∨ t = π ∨ t = 5/3π Dat geeft respectievelijk x = 1 ∨ x = 1 ∨ x = -1/2 - 1/2√3 ∨ x = 1 ∨ x = -1/2 + 1/2√3 Voor punt P is x = -1/2 - 1/2√3 |
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| b. | x
= cos(2t) - sin(2t) x '= -2sin(2t) - 2cos(2t) dus x'(0) = -2 en x '(π) = -2 y = sin(2t) - sin(t) y' = 2cos(2t) - cos(t) dus y '(0) = 1 en y '(π) = 3 |
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| α = cos-1(7/√65) = 29,7° | |||||
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© h.hofstede (h.hofstede@hogeland.nl) |
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