Article: By relying on mathematical calculations, your graph does not need to be as neatly drawn. You do not need to determine any measurement scale. Just sketch a ray in the general direction of your vector. Label your sketched vector with its magnitude and the angle that it makes from the horizontal.  For example, consider a rocket that's being fired upwards at a 60-degree angle, at a velocity of 1,500 meters (5,000 ft) per second. You would sketch a ray that points diagonally upward. Label its length “1500 m/s” and label its base angle “60°.” The diagram shown above indicates a force vector of 5 Newtons at an angle of 37 degrees from the horizontal. Sketch a horizontal ray beginning at the base of your original vector, pointing in the same direction (left or right) as the original. This represents the horizontal component of the original vector. Sketch a vertical ray that connects the head of your horizontal vector to the head of your original angled vector. This represents the vertical component of the original vector. A vector's horizontal and vertical components represent a theoretical, mathematical way of breaking a force into 2 parts. Imagine the child's toy Etch-a-Sketch, with the separate "Vertical" and "Horizontal" drawing knobs. If you drew a line using only the "Vertical" knob and then followed with a line using only the "Horizontal" knob, you would end at the same spot as if you had turned both knobs together at exactly the same speeds. This illustrates how a horizontal and vertical force can act simultaneously on an object. Because the components of a vector create a right triangle, you can use trigonometric calculations to get precise measurements of the components. Use the equation:  sin⁡θ=verticalhypotenuse{\displaystyle \sin \theta ={\frac {\text{vertical}}{\text{hypotenuse}}}} For the missile example, you can calculate the vertical component by substituting the values that you know, and then simplifying, as follows:  sin⁡θ=verticalhypotenuse{\displaystyle \sin \theta ={\frac {\text{vertical}}{\text{hypotenuse}}}} sin⁡(60)=vertical1500{\displaystyle \sin(60)={\frac {\text{vertical}}{1500}}} 1500sin⁡(60)=vertical{\displaystyle 1500\sin(60)={\text{vertical}}} 1500∗0.866=vertical{\displaystyle 1500*0.866={\text{vertical}}} 1,299{\displaystyle 1,299}   Label your result with the appropriate units. In this case, the vertical component represents an upward speed of 1,299 meters (4,000 ft) per second. The diagram above shows an alternate example, calculating the components of a force of 5 Newtons at a 37 degree angle. Using the sine function, the vertical force is calculated to be 3 Newtons. In the same way that you use sine to calculate the vertical component, you can use cosine to find the magnitude of the horizontal component. Use the equation:  cos⁡θ=horizontalhypotenuse{\displaystyle \cos \theta ={\frac {\text{horizontal}}{\text{hypotenuse}}}} Use the details from the missile example to find its horizontal component as follows:  cos⁡θ=horizontalhypotenuse{\displaystyle \cos \theta ={\frac {\text{horizontal}}{\text{hypotenuse}}}} cos⁡(60)=horizontal1500{\displaystyle \cos(60)={\frac {\text{horizontal}}{1500}}} 1500cos⁡(60)=horizontal{\displaystyle 1500\cos(60)={\text{horizontal}}} 1500∗0.5=horizontal{\displaystyle 1500*0.5={\text{horizontal}}} 750{\displaystyle 750}   Label your result with the appropriate units. In this case, the horizontal component represents a forward (or left, right, backward) speed of 750 meters (2,000 ft) per second. The diagram above shows an alternate example, calculating the components of a force of 5 Newtons at a 37 degree angle. Using the cosine function, the horizontal force is calculated to be 4 Newtons.
What is a summary of what this article is about?
Construct a rough sketch of the original vector. Sketch and label the component vectors. Use the sine function to calculate the vertical component. Use the cosine function to calculate the horizontal component.