Skip to Content Go to sign in Skip to Primary Navigation Skip to Secondary Navigation Skip to Page Navigation Skip to Header Navigation Skip to Footer Navigation Read more about accessability options and our navigation

Physics Classroom is making strides to make our site accessible to everyone. Our site contains 6 navigation areas. The Primary, Secondary, and Page Level navigations have a screen reader version of their nav structure that allows using the left and right keys to navigate sibling navigation items, and up or down keys to navigate parent or child navigation items. The others can be navigated using tabs. The Primary Navigation handles the first 2 levels of site pages. The Secondary (which is not always available) handles the 3rd and 4th level of structure. The Page level navigation allows you to navigate the current page's headings quickly. The Header Navigation contains the Light/Dark Mode toggle, Search, Notifications and account login. The Breadcrumb Navigation contains the breadcrumb of the current page. If the current page has a breadcrumb, you can get to it by skipping to the content and tabbing in reverse (shift plus tab). The Footer Navigation contains links such as Privacy, Contact, about and terms. Some resources contain an Audio Player that can be activated by holding down the T key for 3 seconds, and then using K to pause and resume. While not every area of Physics Classroom is usable purely from keyboard and screen reader, we are committed to continue work on making this possible. If you have questions or need additional help, please use this link to contact us.

Return to screen reader navigation
Home Minds On Vectors and Projectiles Mission VP5 Vector Components Help Help 8

Mission VP5 Vector Components

The Question

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.

Define Help

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

Think About It

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.

Math Magic

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)

Hot Link