Weight components of an object on an inclined plane?

My textbook states that the the weight components of an object on an inclined plane are (cos)(angle)x weight and (sin)(angle)x weight. Can you tell me how this is derived?Weight components of an object on an inclined plane?
To understand this you have to look at a picture. I can't really dray one so you'll have to draw it yourself as I explain.


1) Draw a right triangle (your inclined plane) with the smallest angle on the left and the 90 degree angle on the right. (The smallest angle is the one that is used to derive the components)





2)Then draw an object on the inclined plane. Then draw the force of gravity on the object by drawing an arrow going straight down from the object. Label this arrow ';weight.';





3) Next force is the Normal Force. This arrow is perpendiuclar to the inclined plane, going up, and is labeled ';Fn';





4) The components of the weight are the final forces on the object (assuming there's no friction). The sin (angle) x weight is the arrow that is parallel to the plane going down toward the ground, and the cos (angle) x weight is the one that opposes the normal force.





5)The cos (angle) x weight component is equal to the Normal Force. After you draw these arrows then you can make triangles. From these triangle you find out why the components are what they are. However, if you do it this way you need to make sure the arrows are the correct relative lengths. The ';Wieght'; Force must be a projection onto the components of itself so it will become the hypotenuse of the triangles formed.





Hope this helps. Good Luck!Weight components of an object on an inclined plane?
Draw a plane with a weight on it. Then draw the force vectors, one down the plane, one normal to it pointing down. Connect the vecotrs to make a triangle. The hypotenuse (which you just drew) is equal to the sum of the vecotrs. Now can you see how the component formulas are derived?