Chapter 6 (6.1 to 6.2)

Question 1

How do you find the area of a triangle given SAS?

Answer 1

1/2 * outer side * outer side * sine of inner angle

Question 2

What are the two laws of cosines and when do you use either?

Answer 2

Side given SAS- a^2=b^2+c^2-2bccos(a)

Angle given SSS-
Cos A- (b^2+c^2-a^2)/(2bc)

Question 3

How do you find the area of a triangle given SSS?

Answer 3

S=(a+b+c)/2

Area=square root of s(s-a)(s-b)*(s-c)

Question 4

What is the law of sines and when do you use it?

Answer 4

Sin A/a = Sin B/b = Sin C/c

ASA, AAS, SSA (0,1,2 triangles)

Question 5

How do you find the components of a vector given the initial and terminal points?

Answer 5

Terminal x - First x, Terminal y - First y

Question 6

How do you find the magnitude of a vector?

Answer 6

Square root of x^2 plus y^2 (if given component form)

Question 7

If the component form of a vector u is u1,u2 what is the component from of 3u?

Answer 7

3u1, 3u2

Question 8

How do you add vectors given the component form of both? U= 0,3 and V=1,3
How do you add vectors given a picture?

Answer 8

Add the x’s and the y’s (0+1, 3+3 yields 1,6)

Attach the arrow side of one to the point side of another

Question 9

How do you draw a negative vector?

Answer 9

Same vector but in the opposite direction

Question 10

How do you find the unit vector given the component form of a vector?

Answer 10

Unit vector = (u1/{{u}}, u2/{{u}}) or the vector divided by its magnitude

Question 11

How do you check a unit vector?

Answer 11

Make sure its magnitude equals one

Question 12

What is the standard unit vector for i?

Answer 12

1,0

Question 13

What is the standard unit vector for j?

Answer 13

0,1

Question 14

How do you find the linear combination for a given vector?

Answer 14

If v= v1,v2 then the linear combination is v1i, v2j

Question 15

How do you measure the direction angle?

Answer 15

Start from the x-axis, then move counter-clockwise

Question 16

How do you find a direction angle given a linear combination when you have one vector?

Answer 16

First coefficient divides the last coefficient and tan^-1 (Tan theta is y/x)

Question 17

If a vector is on a circle that is not the unit circle, how do you find the linear combination?

Answer 17

Multiply the magnitude by cos theta (for x) and by sin theta (for y) if given the inner angle

Question 18

What is the geometric definition for a dot product?

Answer 18

Magnitude of u and magnitude of v times the cos of theta

Question 19

What is the algebraic definition for a dot product?

Answer 19

For vectors u and v: U dot V = u1v1 + u2v2

Question 20

What is v dot v?

Answer 20

The magnitude of v squared

Question 21

How do you find the slope of a vector?

Answer 21

Divide the y of its component form by x (rise/run)

Question 22

What would the relationships of the slopes be if two vectors were perpendicular (orthogonal)?

Answer 22

Opposite recipricals

Question 23

What would the dot product be of two orthogonal vectors be?

Answer 23

0

Question 24

What is the standard form of a complex number?

Answer 24

A + Bi

Question 25

What is the trig form of a complex number?

Answer 25

Magnitude (cos theta, i*sin theta)

Question 26

How would would plot a complex number?

Answer 26

Real is x-axis, imaginary is y-axis

Question 27

How do you multiply vectors in trig form?

Answer 27

Multiply the magnitude, add the angle

Question 28

How do you divide vectors in trig form?

Answer 28

Divide the magnitude, subtract the angle

Question 29

How do you raise a vector by a power in trig form?

Answer 29

Raise the magnitude by the power, multiply the angle by the power

Question 30

How do you take a root of a complex number and what form does it need to be in?

Answer 30

Trig

Root of magnitude (cos (theta plus 360k/n) + i sin (theta plus 360k/n)) where k is 0 to n-1

Question 31

30, 45, 60* sin and cos

Answer 31

30- s=1/2, c=square3/2
45- s/c square of 2/2
60- c=1/2, s= square3/2