![]() The Calculate activities pull all of the concepts and skills together to calculate the mag/dir or components to one-tenth of a unit. It is also a critical skill in catching the “garbage in, garbage out” calculator moments when working with trig functions and the Pythagorean Theorem. This skill is invaluable for physics, since making quality sketches is such a critical step in solving any type of motion problem, and trigonometry too. The Estimate activities provide practice estimating where the vector is located without the focus on high precision. Whichever variable is selected, it loops through the range of possible values, updating the display automatically to highlight the conceptual nature of vectors.Īny image displayed while using the View activities may be saved for practice, review, or test problems. To create a new vector, click on the graph, or select a variable to loop. The View activities (view vector, components, or both) focus on how magnitude and direction the axial/directional components and right triangles define vectors, as well as how each is spatially connected to the other. Opposite = X component = Magnitude * sin(Direction ) = 5.0 * sin(60º) = 4.3 EastĪnd to calculate the North/South (or Y) component:Īdjacent = Y component = Magnitude * cos(Direction ) = 5.0 * cos(60º) = 2.5 North To find the component in the East/West direction (or X): This means the side opposite 60º is parallel to the x-axis (East/West), and the adjacent side is parallel to the y-axis (North/South). The vector drawn on the right is 60º clockwise from the y-axis (which is north when using the convention for navigation). To convert magnitude and direction to the axial components, use trig equations. In all cases, the hypotenuse will be the magnitude of the vector. First, identify the angle to an axis of interest and then apply the appropriate trig function. This spatial relationship means that we use trig functions to find the axial components of vectors if we know the magnitude and direction. Since the axes that define the direction of a vector are perpendicular to each other, a right triangle also describes a vector relative to the axes. ![]() Tangent( θ) = tan( θ ) = H / W = opposite / adjacent = sin( θ ) / cos( θ )Ĭalculating Vector Components from Magnitude & Direction In addition, there is a function that involves both the sin and cos functions. The ratio W/L is the cosine of θ :Ĭosine( θ ) = cos( θ ) = W / L = adjacent / hypotenuse The base of the triangle, W, is also significant in other physical phenomena. Sine( θ ) = sin( θ ) = H / L = opposite / hypotenuse ![]() When a quantity keeps appearing in a calculation’s final form, mathematicians, scientists, and engineers pay attention. Both H/L and θ indicate the pitch or slope of the ramp. Both triangles have the same angle of inclination, θ. This means that its hypotenuse is only L. Insert a similar right triangle a vertical side length of H. For instance, consider the large right triangle with hypotenuse 2L and vertical side length 2H. When analyzing variables associated with right triangles, the ratio, H/L, keeps popping up again and again.
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