How to Calculate X and Y Components of Vectors

Velocity, acceleration, and force all use vectors to describe their magnitude and direction. Determine the size of horizontal and vertical components of vectors for your next physics or trig lab.

Instructions

  • TIP: Using the previous example of 45 Newtons and a 30 degree angle, the equation would be 45 cosine 30 degrees.
  • Step 1: Use a graphing calculator to find the cosine of the angle and then multiply that value by the magnitude of the vector to find the x component. Type yourself a little smiley face on your calculator and bask in trigonometric glory.
  • FACT: Computer animators and game developers use vectors to determine how objects should be colored and to create movement of light and wind for a realistic appearance.
  • Step 2: Write an equation that shows the magnitude multiplied by the cosine of the angle to determine the value of the horizontal, or x, component.
  • Step 3: Use a graphing calculator to determine the sine of the angle and then multiply that value by the magnitude of the vector to find the y component.
  • Step 4: Draw a vertical and horizontal line from the ends of the vector to form a right triangle. Label the vertical component "v" and the horizontal component "u".
  • Step 5: Write an equation that shows the magnitude multiplied by the sine of the angle to determine the value of the vertical, or y, component.
  • TIP: For example, if the magnitude is 45 Newtons and the angle is 30 degrees. The equation would be written 45 sin 30 degrees.
  • Step 6: Determine the magnitude and angle of the vector.

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