How can we resolve a vector into two 2 components , sin and cos ?

Asked by  | 21st Jun, 2008, 07:35: PM

Expert Answer:

  1. Construct a rough sketch (no scale needed) of the vector in the indicated direction. Label its magnitude and the angle which it makes with the horizontal.
  2. Draw a rectangle about the vector such that the vector is the diagonal of the rectangle. Beginning at the tail of the vector, sketch vertical and horizontal lines. Then sketch horizontal and vertical lines at the head of the vector. The sketched lines will meet to form a rectangle.
  3. Draw the components of the vector. The components are the sides of the rectangle. The tail of each component begins at the tail of the vector and stretches along the axes to the nearest corner of the rectangle. Be sure to place arrowheads on these components to indicate their direction (up, down, left, right).
  4. Meaningfully label the components of the vectors with symbols to indicate which component is being represented by which side. A northward force component might be labeled Fnorth. A rightward force velocity component might be labeled vx; etc.
  5. To determine the length of the side opposite the indicated angle, use the sine function. Substitute the magnitude of the vector for the length of the hypotenuse. Use some algebra to solve the equation for the length of the side opposite the indicated angle.
  6. Repeat the above step using the cosine function to determine the length of the side adjacent to the indicated angle.

Answered by  | 24th Jun, 2008, 01:02: PM

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