![]() ![]() That and it looks like it is getting us right to point A. Our center of rotation, this is our point P, and we're rotating by negative 90 degrees. Which point is the image of P? So once again, pause this video and try to think about it. Than 60 degree rotation, so I won't go with that one. A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point. And it looks like it's the same distance from the origin. Like 1/3 of 180 degrees, 60 degrees, it gets us to point C. So does this look like 1/3 of 180 degrees? Remember, 180 degrees wouldīe almost a full line. One way to think about 60 degrees, is that that's 1/3 of 180 degrees. ![]() So this looks like aboutĦ0 degrees right over here. Since ( 90 ) + 90, this gives us: We now consider rotating an angle by 180. P is right over here and we're rotating by positive 60 degrees, so that means we go counterĬlockwise by 60 degrees. We could use another geometric argument to derive trigonometric relations involving 90, but it is easier to use a simple trick: since Equations 1.5.1 - 1.5.3 hold for any angle, just replace by 90 in each formula. It's being rotated around the origin (0,0) by 60 degrees. Which point is the image of P? Pause this video and see We call this point the center of rotation. That point P was rotated about the origin (0,0) by 60 degrees. More formally speaking, a rotation is a form of transformation that turns a figure about a point. I included some other materials so you can also check it out. (Anti-clockwise direction is sometimes known as counterclockwise direction). To rotate a shape we need: a centre of rotation an angle of rotation (given in degrees) a direction of rotation either clockwise or anti-clockwise. There are many different explains, but above is what I searched for and I believe should be the answer to your question. What are rotations Rotations are transformations that turn a shape around a fixed point. There is also a system where positive degree is clockwise and negative degree anti-clockwise, but it isn't widely used. Product of unit vector in X direction with that in the Y direction has to be the unit vector in the Z direction (coming towards us from the origin). Clockwise for negative degree.įor your second question, it is mainly a conventional that mathematicians determined a long time ago for easier calculation in various aspects such as vectors. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |