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3 years ago

Use trigonometry to resolve the following vectors into components. Describe the vectors using vector

Mathematics

1 answer:

Elodia [21]3 years ago

8 0

Answer:

v ≈ (3.28512, 20.74146)

Step-by-step explanation:

v = 21(cos(81°), sin(81°))

v ≈ (3.28512, 20.74146) . . . . (x, y) components

The notation varies among authors. The vector can be written as ...

(r, θ) = (21, 81°)

r∠θ = 21∠81°

r cis θ = 21 cis 81°

v = 21·e^(i·9π/20)

(x, y) ≈ (3.28512, 20.74146)

v = 3.28512i +20.74146j . . . . perhaps this is the vector notation you want (i and j are unit vectors in the x- and y-directions, respectively)

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Triangle FGH with vertices F(6,6), G(8,8), and H(8,3): (a) Reflection: in the line x = 5 (b) Translation: (x,y)→ (x - 7, y - 9)

irakobra [83]

(a) The vertices after the reflection in the line x = 5 are F'(4,6) , G'(2,8) , H'(2,3) .

and (b) after translation , the vertices are F''(-1,-3) , G'' (1,-1) , H''(1,-6) .

In the question a triangle FGH with vertices F(6,6) , G(8,8) and H(8,3) is given

Part (a)

the rule for reflection of point (x,y) by the line x = p is

(x,y) → (2×p - x , y)

reflection by the line x = 5 ,

we get

the vertices as

$F'$ (2×5-6,6) = (4,6)

G'(2×5-8,8) = (2,8)

H'(2×5 - 8 ,3) = (2,3)

Part (b)

the rule of translation is given as (x,y)→ (x - 7, y - 9)

So , the vertices after translation are

F''(6-7 , 6-9) = (-1,-3)

G''(8-7,8-9) = (1,-1)

H''(8-7,3-9) = (1,-6)

Therefore , (a) The vertices after the reflection in the line x = 5 are F'(4,6)

G'(2,8) , H'(2,3) .

and (b) after translation , the vertices are F''(-1,-3) , G'' (1,-1) , H''(1,-6) .

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