Vectors and Projectiles - Mission VP5 Detailed Help

Consider the vector shown below. The magnitude and direction of the vector is known. To trigonometrically determine the x-component, the ____ function would be used; and to trigonometrically determine the y-component, the ____ function would be used.



 
Definition of Vector Component
A vector component is a projection of a vector onto the horizontal or vertical axis.


 
The components of a vector are often represented on a diagram by constructing a right triangle about the vector such that the vector is the hypotenuse of the right triangle. The components are then the legs of the right triangle. (You have likely seen such diagrams and you might make an effort to sketch one now.) If the vector is a northeast vector, then it has components stretching east and north. The east and north components are simply the east and north legs of the triangle which has been created from the northeast vector.
 
Trigonometric functions can be used to determine the precise magnitude of the legs of these triangles. If the angle Theta is the angle between the eastern axis and the vector, then the leg adjacent the angle Theta is the x-component and the leg opposite the angle Theta is the y-component. Thus, the cosine function is used to calculate the x-component and the sine function is used to calculate the y-component.


 
SOH CAH TOA
The trigonometric functions sine, cosine and tangent can be used to express the relationship between the angle of a right triangle and the lengths of the adjacent side, opposite side and hypotenuse. The meaning of the three functions are:
 
sine Theta= (length of opposite side / length of hypotenuse)
cosine Theta= (length of adjacent side / length of hypotenuse)
tangent Theta= (length of opposite side / length of adjacent side)