Download 2.3 Vectors in Standard Position

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.