Objectives: Work with vectors in standard position. Apply the basic concepts of right-triangle trigonometry using displacement vectors.

 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 65 o  w = 33 m at 135 o  u = 43 m at 214 o  t = 35 m at 338 o

Finding the Components of a Vector  Review of Trig functions  Remember SohCahToa

 Example 1: Find the x- and y-components of the vector v = 10.0 m at 60.0 o

 Example 2: Find the x- and y-components of the vector w = 13.0 km at o.

 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:  v x = v cos   v y = v sin 

 Example 3: Find the x- and y-components of the vector v = 27.0 ft at 125 o.

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 mi and y-component is mi.

 Example 6: Find vector R in standard position with R x = -115 km and R y = +175 km.