|
|||||
| 1. | AP =
√(22 + 12) =
√5 = AQ sin(α + θ) = 2/Ö5 en cos(α + θ) = 1/Ö5 sinα = 1/Ö5 en cosα = 2/Ö5 sin(α + θ) = sinαcosθ + cosαsinθ 2/√5 = 1/√5 • cosθ + 2/√5 • sinθ 2 = cosθ + 2sinθ ...... (1) |
 |
|||
| cos(α
+
θ) = cosαcosθ
- sinαsinθ 1/√5 = 2/√5 • cosθ - 1/√5 • sinθ 1 = 2cosθ - sinθ .......(2) uit (1) volgt cosθ = 2 - 2sinθ invullen in (2): 1 = 2(2 - 2sinθ) - sinθ 1 = 4 - 5sinθ 5sinθ = 3 sinθ = 3/5 |
|||||
| 2. | a. | cost + cos(2t)
= 0 cost + cos(t + t) = 0 cost + costcost - sintsint = 0 cost + cos2t - sin2t = 0 cost + cos2t - (1 - cos2t) = 0 cost + 2cos2t -1 = 0 Noem nu cost = p dan staat er 2p2 + p - 1 = 0 Dat geeft p = 1/2 ∨ p = -1 cost = 1/2 ∨ cost = -1 t = 1/3π ∨ t = 12/3π ∨ t = π Snijpunten (0, √3) en (0, -√3) en (0,0) |
|||
| b. | Pythagoras: A2 = x2 + y2 = (cost + cos2t)2 + (sint + sin2t)2 = cos2t + 2cost • cos2t + cos22t + sin2t + 2sint • sin2t + sin22t = (cos2t + sin2t) + (cos22t + sin2 2t) + 2(cos2t • cost - sin2t • sint) = 1 + 1 + 2cos(2t - t) = 2 + 2cost |
||||
|
© h.hofstede (h.hofstede@hogeland.nl) |
|||||