Download Day 13 Unit 6 Review WS

Accel. Pre-Calculus
Unit 6 Review – Vectors, Polar, Parametric
1. vectors
a. unit vector
b. sum, difference and scalar multiplication
c. dot product (scalar product)
d. angle between two vectors
e. orthogonal, parallel, or neither
f. cross product (vector product)
g. equation of a plane given 3 points on the plane
2. trigonometric form
a. change from standard to trigonometric form and vice versa
b. multiply, divide, raise to a power
c. find roots, solve
6


a. change to standard form 3  cos  i sin 
b. Find the power 2  3i 
3
3

c. Find the sixth roots of 729i
d. Solve x 3  8i  0
3. Parametric
a. Sketch the curve represented by the parametric equation and, where possible, write the
corresponding rectangular equation by eliminating the parameter.
1
x  6cos 
x  1  4t
x 
i.
ii.
iii.
t
y  6sin 
y  2  3t
y t 2
4. Polar
a. plot
b. change from polar to rectangular and vice versa
c. graph


7 

a. Find the corresponding rectangular coordinates for the point: i.  5, 
 , ii.  12,  
6 
2


b. Find two sets of polar coordinates for the point for 0    2 : i.  0, 9  , ii.  5, 5 
c. Convert the polar equation to rectangular form: i. r  5 , ii. r  3cos
d. Convert the rectangular equation to polar form: i. x 2  y 2  9 , ii. y  6 , iii. x 2  y 2  4x  0
e. Graph: i. r  5 , ii.  

2
, iii. r  5cos , iv. r 2  4sin2 2 , v. r 2  cos2
Answer to
3 3 3

i
2
2
2b: 2035  828i

7
11
5
19
23
2c: 3cis ,3cis
,3cis
,3cis
,3cis
,3cis
4
12
12
4
12
12
2a:
2d: 2i ,  3  i , 3  i
3ai: y  
3
11
x 
4
4
3aii: y 
1
x2
3aiii: x 2  y 2  36
 5 3 5


   3 
3  
7 
4ai:  
4bii:  5 2,
,  4aii:  0, 12  4bi:  9,  ,  9,
,  5 2,




2 2 
2  2 
4  
4 



4ci: x 2  y 2  25 4cii: x 2  y 2  3x 4di: r  3 4dii: r  6csc 4diii: r  4cos
4ei:
4eii:
4eiv:
4ev:
4eiii: