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Objectives: •Work with vectors in standard position. •Apply the basic concepts of right-triangle trigonometry using displacement vectors. 2.3 VECTORS IN STANDARD POSITION Recall that vectors may be placed anywhere in a number plane as long as ….. Standard position for a vector: Initial point at origin Expressed in terms of Length Angle measured counterclockwise from the positive x-axis. Sketch the following displacement vectors in standard position. V = 38 m at 65o w = 33 m at 135o u = 43 m at 214o t = 35 m at 338o Finding the Components of a Vector Review of Trig functions Remember SohCahToa sin side adjacent t o angle hypotenuse cos side opposite to angle hypotenuse tan side opposite to angle side adjacent t o angle Example 1: Find the x- and y-components of the vector v = 10.0 m at 60.0o Example 2: Find the x- and y-components of the vector w = 13.0 km at 220.0o. To find the x- and y-components of a vector v given in standard position. Sketch the right triangle with the legs being the x- and y-components of the vector. Find the lengths of the legs of the right triangle as follows: vx = v cos vy = v sin Example 3: Find the x- and y-components of the vector v = 27.0 ft at 125o. Finding a Vector from Its Components To find a vector from its x- and y-components: Sketch x- and y-components and the resultant. Find the acute angle of the right triangle whose vertex is at the origin using the tangent function. Find the magnitude of the vector using the Pythagorean theorem. Example 5: Find the vector R in standard position whose x-component is +7.00 mi and y-component is -5.00 mi. Example 6: Find vector R in standard position with Rx = -115 km and Ry = +175 km.