Pre-Calc Unit 6

Vector Magnitude and Angle

100

How do you make the number seven even?

Remove the s!

200

Use the angle and magnitude to find the vector

theta=22^o

||v||=8

<8cos(22),8sin(22)>

<7.42,2.997>

300

Given the vector <3,5>, Find the magnitude and angle

||v||=sqrt34

theta=arccos(3/sqrt34)

theta=59.04^o

400

Use the angle and magnitude to find the vector

theta=56^o

||v||=4

<4cos(56),4sin(56)>

<2.24,3.32>

500

Given the vector <-2,-4>, Find the magnitude and angle

||v||=sqrt20

theta=arccos(2/sqrt20)

theta=63.43^o" in Q1"

angle=180+63.43

angle=243.43^o

Vectors and Angle Between

100

Which king loved fractions?

"Henry the "1/8

200

Find and Graph the vector from the initial point (5,-2) and terminal point (2,-4)

<-3,-2>

300

Find the dot product of <2,3> and <-1,6>

16

400

Find the angle between two vectors u=<-1,3> and v=<2,4>

45^o

500

Find the angle between two vectors u=<-4,5> and v=<3,3>

83.66^o

Projection Vectors

100

What do you get if you divide the circumference of a jack-o-lantern by its diameter?

Pumpkin Pi!

200

"Find " u_2 if u=<4,2> and proj_vu=<2,1>

<2,1>

300

"Find " u_2 if u=<5,3> and proj_vu=<3.2,1.7>

<1.8,1.3>

400

"Find "proj_vu " if u=<2,3> and v=<4,6>

proj_vu=1/2<4,6>

proj_vu=<2,3>

500

"Find "proj_vu " if u=<1,3> and v=<5,4>

<2.07,1.66>

Parametric Equations

100

Why can’t you trust a math teacher holding graphing paper?

They must be plotting something

200

Make a table for -2<t<2 for the following parametric equations

x=2t-3

y=t^2+1

t        x        y

-2      -7      5

-1      -5      2

0.       -3.    1

1.       -1.     2

2.        1.      5

300

Make a table for -2<t<2 for the following parametric equations

x=3t+2

y=t^3-5

t.       x.        y

-2.     -4.     -13

-1.     -1.      -6

0.       2.      -5

1.       5.       -4

2.       8.       3

400

Eliminate the parameter for the following parametric equations

x=2t-3

y=t^2+1

y=((x+3)/2)^2+1

500

Eliminate the parameter for the following parametric equations

x=3t+2

y=t^3-5

y=((x-2)/3)^3-5

Graphing Polar Coordinates

100

"Why did " 1/5"th go to the masseuse?"

Because he was two-tenths!

200

How are the points listed for polar coordinates?

(r,theta)

r=radius

theta="angle"

300

When graphing polar coordinates, what do you do if r is negative?

Go the opposite direction from the origin on the line created by the angle

400

Graph the polar coordinate

(4,60^o)

On 60^o angle, 4 away from origin

(In Q1)

500

Graph the polar coordinate

(-3,300^o)

3 circles away from origin, on 300^o line in opposite direction

(In Q2)