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.
- 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.