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Finding Vector Components with Trig Functions

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Basics of finding the X and Y components of a Vector along with verifying the angle and the sides

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good morning today we're going to learn about component vectors by breaking a displacement Vector into its Vector components. smokerlyzer racer go through a displacement of 90.0 cm and an angle of 32 degrees north of East Point backers displacement in the extra where do you sell packs and displacement in the y direction or the sub Watt help me find directions for DNA extraction how can we find either of these two sides of the triangle is a right triangle so so kind beta-sol sign is opposite over hypotenuse and opposite direction the hypotenuse of the triangle is D we want to solve 14 Vital Signs By Dee Dee in the y direction equals d x a sign of we can substitute in numbers so we times the sine of 32 degrees for 49 6287 actually do know it's 47.69 37628 my calculators and you don't even have a calculator I'm sure your calculator is in radian mode in order to deceive your calculator in degree mode we can use the stack of sine theta equals opposite over hypotenuse to solve for displacement in the y direction because our angle of 32° only had two significant digits we should have to answer for 48 cm for the displacement in the Y Direction X Dean get the displacement in which direction equals d x a cosine of angle is that works out to be 90 times a cosine of 32 which is 76.324 with 2 sig figs 76 cm is traffic was adjacent over hypotenuse to solve for the displacement in the X Direction which is 76 centimeters why are the components of record into those components Some people prefer to break the heart is so much more fun to say bread weird it is important to understand what it means that diesel accent diesel why are the components of a vector D this mean that when you add Vector DNA extraction to Vector G in the y direction you get the vector we can show this visual using our slow velocity racer first we can have her travel the component that is the displacement reaction reaction or 76cm in the positive X Direction and then we can talk slow velocity racer 90° and have her travel the component that is the displacement meters into I know. Exact same spot as the original display skip back 30 again this is because the components of vector d d sub X & D Supply the original Vector D which means that that Saturday is the resultant Vector Halo won't slow velocity racer be facing in a different direction when she gets to the final point I don't see how it's the same thing then good question but we actually have to go back to the definition of displacement in order to answer your question to Billy what is the definition of displacement displacement is the straight-line distance between the displacement only depends on the initial in final points the past is irrelevant so the direction facing doesn't matter I got it Direction diesel by doing this problem in reverse I want you to do is going to stop by figuring out the magnitude of vector d by using the Pythagorean theorem a squared plus b squared equals c squared directions we're blessed in Swissvale in the y-direction squared equals the displacement Square taking the square root of bolts equals the square root of the word erection Square substituting in numbers 47.693 squared the square root of a whole thing works out to be 89.894 CM the magnitude of the displacement Gandrud change your fate equals opposite over adjacent angle Theta is the displacement of the y direction adjacent is the displacement in the X Direction take an inverse tangent of outside Phoenix equal to the intersection of displacement divided by displacement in extra action substituting a number state is equal to the inverse tangent of 47.693 divided by 76.324 31.892 degrees four to Six Flags because our original angle only have we get our displacement of 90 CM or 9.0 x 10 to the 1st the mango 32 degrees north of East which is the same as our original displacement Vector with two sig figs because again the components of a vector d add up to the original Vector d That's what it means to be the components of a vector that makes sense but I still have a question about the displacement directions magnitude and Direction Saudis is 76cm just be the magnitude without the direction as a question bottom has both magnitude and Direction here is how this which direction in the fact that the number is positive means it's in the positive X Direction so in the X direction of 76cm literally means that this is a displacement of 76 cm the positive X Direction so decent y equals 48 CM means it's a displacement in the positive y direction of 48cm Direction Just so you know this concept of breaking resolving a vector into its components is a concept that you're going to use for the rest of your physics careers no matter how long we last questions answer review sine and cosine to figure out the pieces of your deal are the components of a vector D literally equals the original this place because that's what it means to be a component of a rat you are a piece of the original Vector thank you very much for going with me today I enjoyed learning with you

Uploaded by Shawn Mize.

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Finding Vector Components with Trig Functions

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