The-Organic-Chemistry-Tutor
This video section teaches how to find the X and Y components of a vector given its magnitude and direction by using trigonometry. The instructor explains that the X component is found by multiplying the force by the cosine of the angle, and the Y component is found by multiplying the force by the sine of the angle. This comes from the SOHCAHTOA rule in trigonometry, where sine is opposite over hypotenuse and cosine is adjacent over hypotenuse. The instructor provides examples and demonstrates how to use these equations to find the components of a force vector.
In this section, the video discusses how to find the components of a vector given its magnitude and direction. The first example involves a force vector with a magnitude of 300 Newtons and a direction 30 degrees above the x-axis. To determine the x and y components, the formulas F cosine Theta and F sine Theta are used, respectively. The second example involves a force vector with a magnitude of 200 Newtons and a direction 210 degrees below the x-axis. The angle is measured from the positive x-axis in a clockwise direction, and the appropriate signs for the x and y components are added based on the quadrant.
In this section of the video, the instructor shows how to find the X and Y components of a vector given its magnitude and direction using trigonometry. The X component is equal to the force times the cosine of the angle and the Y component is equal to the force times the sine of the angle. The instructor explains that these equations come from the SOHCAHTOA rule in trigonometry, where sine is opposite over hypotenuse and cosine is adjacent over hypotenuse. By multiplying both sides of the equations by the force, the X and Y components of the vector can be found. The instructor demonstrates how to use these equations to find the components of a force vector and writes the answer in component form.
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