taylor 28 march reflection

so we have to start preparing for the trig exam

so away we go

**The Unit Circle

90 degrees, (0,1), pi/2

180 degrees, (-1,0), pi

270 degrees, (0,-1), 3pi/2

360 degrees, (1,0), 2pi


**6 Trig Functions

sin = y/r

cos = x/r

tan = y/x

csc = r/y

sec = r/x

cot = x/y


**Degrees & Radians

Degrees to radians= Degree * pi/180

Radians to degrees= Radians * 180/pi

**To solve coterminal angles, either add or subtract 360 to the angle

i need a review of the chapter with amplitude and the graphs and other information that goes along with a problem like that

Stephen's Reflection

Ok so this week i think we are learning something new..idk but anyway i do remember trig functions really well because they are really east. there are six trig functions:

6 Trig Functions

sin = y/r

cos = x/r

tan = y/x

csc = r/y

sec = r/x

cot = x/y

theres a few things i do not understand which is law of sines, law of cosines, and sigma notations...

Lima Beans, Hearts, and Roses!

• Limacon - Looks like a lima bean!
• r = a+b sin theta
• r = a+b cos theta

• Cardioid - Looks like a heart!
• a-b sin theta
• a-b cos theta

• Rose - Looks like a ...rose.
• r = a sin (number of petals) theta
• r = a cos (number of petals) theta 

• Archimedes Spiral - The black and white spiral that hypnotizes people in the cartoons.
• r = a theta +b

• Logarithmic Spiral - Looks like a ...spiral.
• r=a^theta b

Alicia's Reflection #32

Alrighty so last week we finished taking our chapter tests. I think this week is ACT prep so hopefully we review ACT stuff in math. I am going to review some trig from Ch. 10.

Law of Sines:

sinA/a = sinB/b = sinC/c

Law of Cosines:
(opp leg)^2 = (adj leg)^2 + (other adj leg)^2 -2(adj leg)(adj leg)cos(angle between)

Example:
x= 6^2 + 5^2 -2(5)(6) cos 36
x=3.530


Here are some formulas:

Cos(α +/- β)=cos α cos β -/+ sin α sin β
sin(α +/- β)=sin α cos β -/+ cos α sin β
sin x + sin y= 2 sin x + y/2 cos x-y/2
sin x - sin y= 2 cos x + y/2 sin x-y/2
cos x + cos y= 2 cos x + y/2 cos x-y/2
cos x - cos y= 2 sin x + y/2 sin x-y/2

tan (α + β)=tan α + tan β/1-tan α tan β
tan (α - β)=tan α - tan β/1+tan α tan β

sin2α=2sin α cos α
cos 2α=cos^2 α –sin^2 α = 1-2 sin^2 α= 2 cos^2 α -1
tan 2α = 2tan α /1-tan^2 α
sin α/2= +/- √1-cos α/2
cos α/2= +/- √1+ cos α/2
tan α/2= +/- √1-cos α or 1 + cos α
=sin α/1+cos α
=1-cos α/sin α

I could use some help with sigma notation

Reflection

So I'm thinking that since B-Rob is suppose to be coming back this week and originally was suppose to be coming back last week we will have A LOTTTT of work to do in order to catch up. I guess I could use it because I really do not remember too much...area of a non right triangle.

Area of a Non Right Triangle:

Formula:1/2(leg)(leg)sin(angle b/w)

So if you had 1/2(3)(6)sin(52) your answer would be: 7.100

Does anyone know what we're suppose to be doing when B-Rob comes back?

Amy's Reflection #32

**Logs

Condense:

Ex) logm + log7 + 4logn

= log7mn^4

Ex) 5loga + logd + log6

= log6da^5

Ex) 4logt - logc

= t^4/c

Ex) logn - 3logh -logy

= n/yh^3

Expand:

Ex) log5gh^2

= log5 + 2logh +logg

Ex) m^3b^7/f

= 3logm + 7logb - logf


**The Unit Circle

90 degrees, (0,1), pi/2

180 degrees, (-1,0), pi

270 degrees, (0,-1), 3pi/2

360 degrees, (1,0), 2pi


**6 Trig Functions

sin = y/r

cos = x/r

tan = y/x

csc = r/y

sec = r/x

cot = x/y


**Degrees & Radians

Degrees to radians= Degree * pi/180

Radians to degrees= Radians * 180/pi

**To solve coterminal angles, either add or subtract 360 to the angle.

can someone help me with how to use law of cosine??

Stephanie's Reflection

Limacon
r = a+b sin theta
r = a+b cos theta

Cardioid
a-b sin theta
a-b cos theta

Rose
r = a sin n theta
r = a cos n theta
n is how many petals

Archimedes Spiral
r = a theta +b

Logarithmic Spiral
r=a^theta b

Converting
polar to rectangular
x=r cos theta
y=r sin theta

rectangular to polar
r=+/- sqrt x^2 + y^2
theta is (x/y)

Trig Chart:

0°
sin0=0
cos0=1
tan0=undefined
sec0=1
cot0=0

30°
sinπ/6=1/2
cosπ/6=√3/2
tanπ/6=√3/3
cscπ/6=2
secπ/6=2 √3/3
cotπ/6=√3

45°
sinπ/4=√2/2
cosπ/4=√2/2
tanπ/4=1
cscπ/4=√2
secπ/4=√2
cotπ/4=1

60°
sinπ/3=√3/2
cosπ/3=1/2
tanπ/3=√3
cscπ/3=2 √3/3
secπ/3=2
cotπ/3=√3/2

90°
sinπ/2=1
cosπ/2=0
tanπ/2=undefined
cscπ/2=1
secπ/2=undefined
cotπ/2=0