Taylor reflection #10

For the blog for week 10 I am posting late because I missed the entire week of notes so I figured I would wait and get help with the hellacious week I expected to follow. However what came this week was surprising. Everyone was having trouble with what was learned the week I was out so we spent the majority of this week reviewing. So far I think I understand the notes. By the time I have to post a blog again I will have a very definitive idea of how I am handling the trig things we have learned so far.
As of right now I definitely understand the trig chart
TRIGCHART
0° *sin 0= 0 *cos 0= 1 *tan 0= 0 *csc 0= undefined *sec 0= 1
*cot 0= undefined

30° * sin π/6= 1/2 *cos π/6= √3/2 *tan π/6= √3/3 *csc π/6= 2 *sec π /6= 2 √3/3
*cot π/6= √3
45° *sin π/4= √2/2 *cos π/4= √2/2 *tan π/4= 1 *csc π/4= √2 *sec π/4= √2
*cot π/4= 1
60° *sin π/3= √3/2 *cos π/3= 1/2 *tan π/3= √3 *csc π/3= 2 √3/3 *sec π/3= 2
*cot π/3= √3/2
90° *sin π/2= 1 * cos π/2= 0 *tan π/2= undefined *csc π/2= 1 *sec π/2= undefined *cot π/2= 0

I also discovered an easier way to memorize the chart
First you would have to set up the chart differently than it was given
It would have to look like this
Sin Cos Tan Csc Sec Cot
30
45
60
90
Just like a graph and then you fill in the parts for each
If you can memorize the sin column for the chart you can figure out the rest of the chart
Cos is just sin backwards
Tan is just sin/cos
Csc is just 1/sin
Etc. You just have to find the relations of each

And that’s all I’ve got so far
Im still trying to learn everything else

Devin's Reflection #10

This week we learned some more trig stuff. We learned some trig functions. The sin and csc both deal with the y factor and radius. The cos and sec both deal with the x factor and radius. The tan and cot both deal with the x factor along and the y factor. Radius is the square root of x(2) + y(2).

The trig functions are:

sin 0= y/r

cos 0= x/r

tan 0= y/x

csc 0= r/y

sec 0= r/x

cot 0= x/y

Unit Circle

2-(0,1)-90-pi/2 1-(1,0)-0,360-0,2pi

3-(-1,0)-180-pi 4-(0,-1)-270-3pi/2

The Trig Chart

0 sin 0=0 cos 0-1 tan 0=0

30 sin pi/6=1/2 cos pi/6= (3)/2 tan pi/6=(3)/3

45 sin pi/4=(2)/2 cos pi/4=(2)/2 tan pi/4=1

60 sin pi/3=(3)/2 cos pi/3= 1/2 tan pi/3=(3)

90 sin pi/2=1 cos pi/2=0 tan pi/2= underined

0 csc 0= undefined sec 0=1 cot 0= undefined

30 sin pi/6=2 sec pi/6=(2) cot pi/6=(3)

45 sin pi/4=(2) sec pi/4=(2) cot pi/4=1

60 sin pi/3=2(3)/3 sec pi/3=2 cot pi/3=(3)/3

90 sin pi/2=1 sec pi/2=undefined cot pi/2=0

Reference angles must be between 0 and 90, 0 and pi/2

1. Find which quadrant angle is in

2. Determine the sign in that quadrant (+ve or -ve)

3. Subtract 180 until the angle is between 0 and 90, 0 and pi/2

We also learned inverses.

To solve for an angle

1. simplify any expression

2. get the trig function by itself

3. take the trig inverse of both sides

4. use chart unit circle or calculator to find 1 angle

5. set up and find other quadrants with the same sign as the value.

Ex. sin -1((2)/2)=45 quadrants 1 and 2

To make from quadrant to quadrant:

1-3 make it -ve and add 360

1-2 make it -ve and add 180

1-4 add 360

2-4 add 180

Alicia's reflection #10

okay so this week wasn't so bad. So far, trig is not as hard as it sounds but I still need to memorize the trig chart.

7-3

sinθ=y/r
cosθ=x/r
tanθ=y/x
cscθ=r/x
secθ=x/y
cotθ=x/y

The equation to use is r=√(x^2+y^2)

***Remember... sin relates to the y axis, cos relates to the x axis, and tan relates to both the x and y axis.

7-4

Memorize this trig chart for the ch. 7 test!!!

0° sin0=0 cos0=1 tan0=0 csc0=undefined sec0=1 cot0=undefined

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

***I have a hard time with the word problems from the homeworks. They really throw me off so if anyone can help with word problems that would really help for the test. Thankss!!



Goodluck on the test :)

I really do understand trig, I just have to take the initiative to study it all.
First:
sin= y/r csc=r/y
cos=x/r sec=r/x
tan=y/x cot=x/y
r=√x^2+y^2
*csc, sec, and cot are opposites of sin, cos, and tan.
*they are used to find θ, an angle measure. (unit circle)

Second:
Trig chart.
It is pretty self explanitory. MEMORIZING it is the hard part. Using it is pretty simple.

Third:
Reference angles.
1. find which quadrant the angle is in.
2. determine the sign in that quadrant
3. subtract 180° until the angle is between the absolute value of 0° and 90°

e.g. Find the reference angle for sin210°
1. lies in quadrant 3
2. sin is negative in quadrant 3
3. 210-180=30
sin210°= -sin30
you would then look to your trig chart and find a reference to sin 30 (π/6)
sin 210°=1/2

I pretty much understand everything. I just need to keep studying. If I have any questions, I'll be sure to ask on Monday.

Stephanie's Reflection

1)s=rθ
2)k=1/2r^2θ (k=1/2rs)
r = radius, θ = angle, s = arc length, k = area of sector

EG: A sector of a circle has an arc length of 6cm and an area of 75cm^2. Find its radius and measure of its central angle.
s=6cm
k=75cm^2
r=?
θ=?
k=1/2rs
75=1/2r6
75=3r
r=25cm
s=r
6=25θ
θ=6/25

sinθ=y/r
cosθ=x/r
tanθ=y/x
cscθ=r/x
secθ=x/y
cotθ=x/y
r=√(x^2+y^2)

EG: sin180° = y/r
at 180°, y=0
0/1 = 0
thus sin180°=0

EG: cosπ/2 = x/r
π/2 is at 90°
at 90°, x=0
thus cosπ/2=0

Trig Chart:
0°
sin0=0
cos0=1
tan0=0
csc0=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

Reference Angles (must be between 0° and 90°)
1)find which quadrant angle is in
2)determine the sign in that quadrant (+ve or -ve)
3)subtract 180° until the angle is between 0° and 90° (0 and π/2)

1)find the reference angle using chart or calculator
2)find what quadrant you need to be in based on the sign of the value
3)use notes to move to that quadrant
To Move:
I to IV = make negative and add 360°
I to III = add 180°
I to II = make negative and add 180°
II to IV = add 180°

EG: sin^-1(-√2/2) = 45°
45 + 180 = 225° = θ
I to IV
-45 + 360 = 315°
θ = 225°, 315°

I believe I mostly caught up with this stuff but I still don't quite understand the last few sections.

Stephen's Reflection

Ok this week was all trig...fun!! (not really). But anyway i think the easiest stuff was writing degrees as ' and ", converting to radians, and converting to degrees. So i guess i will talk about that. The first one im going to talk about is writing degrees as ' and ".
Ex:
write 12.3 degrees as ' and ".
what you do first is separate the numbers before and after the decimal and multiply everything after the decimal by 60
-12 degrees (.3 x 60)
Then your answer would be 12 degrees 18'
*if you multiplied the decimal by 60 and it gave you another decimal number then you would do the same thing as before but you would put " after the answer

Now to convert to radians:
Ex:
36 degrees converted to radians
first you multiply the degrees by pi/180
so you would divide 36 by 180 and you would get a decimal and then you want to convert it to a fraction.
your answer would be 1/5 pi or pi/5

Now to convert to degrees:
Ex:
3pi/4
multiply 3pi/4 x 180/pi..both pi's will cancel
then multiply 3 x 180 all over 4
then your answer would be 135 degrees

Some stuff i will have trouble with is remembering the unit circle and remembering the trig chart. I can remember the degrees part of the unit circle but with the parts with pi but i guess thats kinda my responsibility to remember it but if someone can just help me with it in class or stuff i would be thankful.

This week I was nervous because everyone was telling me that we were starting Trig. and saying that it is really hard. The week started off pretty hard and I did not really understand anything too good but it started getting easier. One thing that I really know, and I'm pretty pumped about knowing, is the Trig Chart.

0° sin0=0 cos0=1 tan0=0 csc0=undefined sec0=1 cot0=undefined

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=√2/2 secπ/4=√2/2 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=√3/3

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


(I swear I did that all by myself off the top of my head =])

One thing that I am struggling in, however, is Sector of a Circle.
I think the thing that is messing me up is how the letters stand for completely different things, like K is the are of a sector.