2 CA content standards: Trigonometry 12.0 Students use trigonometry to determine unknown sides or angles in right triangles.13.0 Students know the law of sines and the law of cosines and apply those laws to solve problems.14.0 Students determine the area of a triangle, given one angle and the two adjacent sides.19.0 Students are adept at using trigonometry in a variety of applications and word problems.
3 OBJECTIVES Represent vectors as directed line segments Write vectors in component formAdd and subtract vectors and represent them graphicallyPerform basic operations on vectors using scalarsWrite vectors as linear combinations of i and jFind the direction angle of a vectorApply vectors to real-world problems
4 Vector Directed line segments Named by initial point and terminal point (like a ray, in geometry)Ex: PQPQ
5 Vectors have direction and magnitude Magnitude = lengthGiven the endpoints of a vector use the distance formula to find its magnitude
6 Vectors with the same direction and magnitude are equal. Vectors can also be named using a single, bold, lowercase letterEx: u=PQ
7 Given P=(0,0) Q=(3,4) R=(4,3) S=(1,2) T=(-2,-2) a=PQ, b=RP, c=ST, d=QP which vectors are equivalent?
8 component form Standard position – initial point at origin Component form – use terminal point to refer to vectorvvyvx
15 Unit vectors Remember a unit vector is any vector with magnitude of 1 To find a unit vector in the direction of a vector v, divide the vector by its magnitudeEx. Find the unit vector in the direction of <5,-2>
16 Unit vectorsA vector can be written in terms of a directional unit vector and its magnitudeWrite in terms of the unit vector w/ the same direction
17 standard unit vectorsHorizontal unit vectorVertical unit vectorji
18 ALL vectors in a plane can be written as a combination of i and j Ex. W has an intial point at (6,6) and terminal point (-8,3) write it as a combination of i and jW in component form is <-14, -3>As a combination of i and j, W = -14i – 3j
19 direction angles and vectors Direction angle is from the positive x axis.Use right triangle trig.vvyθvx