Senin, 09 Februari 2015
Rumus Matematika - Halo berjumpa lagi dengan rumus matematika, pada pembahasan materi
kali ini kita akan membahas mengenai Materi Ruang Dimensi Tiga Matematika SMA Kelas X . pada materi ini ada 3 sub-judul yang akan dibahas, dimulai dari
pembahasan mengenai jarak, lalu pembahasan mengenai sudut, dan yang terakhir
akan diberikan penjelasan mengenai volume bangun ruang. Yuk langsung saja kita
lihat pembahasannya.
Materi Ruang Dimensi Tiga Matematika Tentang jarak, Sudut, dan Volume Bangun Ruang
Jarak
Garis tegak lurus bidang
Merupakan sebuah garis yang posisinya tegak lurus pada suatu bidang
dimana garis tersebut tegak lurus terhadap setiap garis yang ada pada bidang
tersebut.
Jarak titik dan garis
Jarak titik A dengan garis G merupakan panjang ruas dari garis AA'
dimana titik A' merupakan proyeksi dari A pada g.
Jarak titik dan bidang
Jarak antara titik A dan bidang merupakan panjang dari ruas garis AA'
dimana titik A' adalah proyeksi dari titik A pada bidang.
Jarak antara dua garis sejajar
Untuk mengetahui jarak antara dua garis sejajar, kita harus menggambar
sebuah garis lurus diantara keduanya. Jarak titik potong yang dihasilkan
merupakan jarak dari kedua garis itu.
Jarak garis dan bidang yang sejajar
Untuk menentukan jarak antara garis dan bidang adalah dengan membuat
proyeksi garis pada bidang. Jarak antara garis dengan bayangannya adalah jarak
garis terhadap bidang.
Jarak antar titik sudut pada kubus
Jarak antar titik sudut pada kubus dapat diketahui melalui rumus:
diagonal
sisi AC = a√2
diagonal
ruang CE = a√3
ruas
garis EO = a/2√6
Penting untuk diingat:
ketika kalian ingin menentukan jarak, hal yang pertama kali harus kalian
lakukan adalah membuat garis-garis bantu yang membentuk segitiga. dengan begitu
kalian akan lebih mudah dalam mencari jarak yang ditanyakan di dalam soal.
Sudut
Sudut antara garis dan bidang
Sudut antara garis dan bidang adalah sudut yang terbentuk antara garis
dengan bayangannya apabila garis itu diproyeksikan terhadap bidang yang ada di
bawahnya.
Sudut antara dua bidang
Sudut antara dua bidang merupakan sudut yang terbentuk oleh dua buah garis
lurus yang posisinya tegak lurus dengan garis potong pada bidang α dan β
Penting untuk diingat:
Ketika kalian ingin menentukan sudut, hal paling pertama yang harus
kalian lakukan adalah menentukan terlebih dahulu titik potong diantara dua
obyek yang akan dicari sudutnya, setelah itu buatlah garis-garis bantu yang
membentuk segitiga.
MATERI PERSONAL LETTER
Definition:
A type of letter (or informal composition)
that usually concerns personal matters and it is sent from one
individual to another such as family members, relatives and friends, and
love letters. People write and send personal letters for only a small
number of people to read — usually one or two. Writers can send personal
letters for lots of different reasons: short memos for business
strategies, love letters between long-distance sweethearts or even pen
pal messages to foreign exchange students. Senders usually handwrite
personal letters, which emphasizes the personal nature of the note.
Form of a Personal Letter
- Date – This is the date when the letter is written.
- Name, Address, City and Zip Code – these are name, address, city and zip code of the sender.
- Salutation and Name of Recipient – The greeting usually starts with the word ‘Dear’ followed by the given name of the recipient or relationship and it ends with a comma. Two examples are shown: ‘Dear Ronald,’ ‘Dear Uncle,’
- Introduction– This is the opening of a letter. It may include greetings like ‘How are you?’ Sometimes, you may refer to a previous letter.
- Body– This is the main part of the letter. It includes the message that the writer wants to tell the recipient. It is often divided into paragraphs.
- Closure– This part indicates the letter is going to end. The writer may ask the recipient to reply here.
- Complimentary Close– This short expression includes a few words on one line. It ends with a comma. Some examples are shown below. ‘Yours sincerely,’ ‘Best regards,’ ‘Love,’
- Signature– the signature of the writer
Example of personal letter
October,10th 2013
From : Anissa Trimahayanti
Jl. Kenanga, gang Asri II, no 4 Denpasar 29055
My Dearest Friend Lisa,
Lisa, how are you? I hope that you and your family are all right. How about your study? You are my best friend ever. You always understand me though others won’t. When you decided to study in java, I was so confused and sad because a person who always next to me would leave me. I remember the last time we met, you said to me that it would be OK and our friendship would be still good.
During months, I attempted to adapt myself to my new class in Mahasaraswati University. Yeah, finally I could. I found a girl who could support me as well as you. Her name is Dahlia. I felt that I was happy to be her friend because she reminds me with the girl next to me last three months in Senior High School. Yes, she is as the best friend of mine as you. Of course I will introduce her to you.Even though we are now many miles away, I do believe the time when we can get together will come soon, doesn’t it? You should reply “YES”. So that Dahlia, you and me will be three best girls ever in the world. The sooner the better!!!! I miss you so much. I am always longing to see you; moreover, I want to share anything that usually I tell to you like when we were in Senior high school.
Lisa, I do promise to introduce Hendra, the person you admire… :) So, when will you come back?
Please replay my letter as soon as you can because I’m really interested to know about your life here. J
Your old friend,
Anissa
Analysis
Date: October,10th 2013
Name and Address of sender: Anissa Trimahayanti , Jl. Kenanga, gang Asri II, no 4 Denpasar
Salutation and Name of Recipient: My Dearest Friend Lisa,
Introduction: Lisa, how are you? I hope that you and your family are all right. How about your study? You are my best friend ever. You always understand me though others won’t. When you decided to study in java, I was so confused and sad because a person who always next to me would leave me. I remember the last time we met, you said to me that it would be OK and our friendship would be still good.
Body : During months, I attempted to adapt myself to my new class in Mahasaraswati University. Yeah, finally I could. I found a girl who could support me as well as you. Her name is Dahlia. I felt that I was happy to be her friend because she reminds me with the girl next to me last three months in Senior High School. Yes, she is as the best friend of mine as you. Of course I will introduce her to you.Even though we are now many miles away, I do believe the time when we can get together will come soon, doesn’t it? You should reply “YES”. So that Dahlia, you and me will be three best girls ever in the world. The sooner the better!!!! I miss you so much. I am always longing to see you; moreover, I want to share anything that usually I tell to you like when we were in Senior high school.
Closure :Lisa, I do promise to introduce Hendra, the person you admire… :) So, when will you come back? Please replay my letter as soon as you can because I’m really interested to know about your life here. J
Complimentary Close :Your old friend,
Anissa
Introduction to Trigonometry
Trigonometry (from Greek trigonon "triangle" + metron "measure")
Want to Learn Trigonometry?
Here is a quick summary.
Follow the links for more, or go to Trigonometry Index
 |
Trigonometry ... is all about triangles. |
Right Angled Triangle
The right angle is shown by the little box in the corner.
We usually know another angle θ.
And we give names to each side:
- Adjacent is adjacent (next to) to the angle θ
- Opposite is opposite the angle θ
- the longest side is the Hypotenuse
"Sine, Cosine and Tangent"
Trigonometry is good at find a missing side or angle in a triangle.The special functions Sine, Cosine and Tangenthelp us!
They are simply one side of a triangle divided by another.
For any angle "θ":
Sine Function:
|
sin(θ) = Opposite / Hypotenuse |
Cosine Function:
|
cos(θ) = Adjacent / Hypotenuse |
Tangent Function:
|
tan(θ) = Opposite / Adjacent |
(Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)
Example: What is the sine of 35°?
 |
Using this triangle (lengths are only to one decimal place):
sin(35°) = Opposite / Hypotenuse = 2,8/4,9 = 0,57...
|
Example: What is the missing length here?
- We know the Hypotenuse
- We want to know the Opposite
sin(45°) = 0,7071...
Now multiply by 20 (the Hypotenuse length):
Opposite length = 20 × 0,7071... = 14,14 (to 2 decimals)
Try Sin Cos and Tan!
Move the mouse around to see how different angles affect sine, cosine and tangentAnd you will also see why trigonometry is also about circles!
Notice that the sides can be positive or negative according to the rules of Cartesian coordinates. This makes the sine, cosine and tangent vary between positive and negative also.
Unit Circle
What you just played with is the Unit Circle.It is a circle with a radius of 1 with its center at 0.
Because the radius is 1, we can directly measure sine, cosine and tangent.
Here we see the sine function being made by the unit circle:
Degrees and Radians
Angles can be in Degrees or Radians. Here are some examples:| Angle | Degrees | Radians |
|---|---|---|
 Right Angle |
90° | π/2 |
| __ Straight Angle | 180° | π |
 Full Rotation |
360° | 2π |
Repeating Pattern
Because the angle is rotating around and around the circle the Sine, Cosine and Tangent functions repeat once every full rotation.When we need to calculate the function for an angle larger than a full rotation of 2π (360°) we subtract as many full rotations as needed to bring it back below 2π (360°):
Example: what is the cosine of 370°?
370° is greater than 360° so let us subtract 360°
370° − 360° = 10°
cos(370°) = cos(10°) = 0,985 (to 3 decimal places)Example: what is the sine of −3 radians?
−3 is less than 0 so let us add 2π radians
−3 + 2π = −3 + 6,283 = 3,283 radians
sin(−3) = sin(3,283) = −0,141 (to 3 decimal places)Solving Triangles
A big part of Trigonometry is Solving Triangles. "Solving" means finding missing sides and angles.Example: Find the Missing Angle "C"
So C = 180° − 76° − 34° = 70°
When we know any 3 of the sides or angles we can find the other 3
(except for the three angles case)
(except for the three angles case)
See Solving Triangles for more details.
Other Functions (Cotangent, Secant, Cosecant)
Similar to Sine, Cosine and Tangent, there are three other trigonometric functions which are made by dividing one side by another:
Cosecant Function:
|
csc(θ) = Hypotenuse / Opposite |
Secant Function:
|
sec(θ) = Hypotenuse / Adjacent |
Cotangent Function:
|
cot(θ) = Adjacent / Opposite |
Trigonometric and Triangle Identities
And as you get better at Trigonometry you can learn these: |
The Trigonometric Identities are equations that are true for all right-angled triangles. |
 |
The Triangle Identities are equations that are true for all triangles (they don't have to have a right angle). |
Enjoy becoming a triangle (and circle) expert!
Pengertian Descriptive Text
Dalam artian luas, Description, seperti dijelaskan oleh Kane (2000: 352), diartikan seperti pada kalimat di bawah ini :
Description is about sensory experience—how something looks, sounds, tastes. Mostly it is about visual experience, but description also deals with other kinds of perception.
Jadi, jika disimpulkan dari penjelasan Kane di atas, tulisan deskriptif bermakna
teks yang menjelaskan tentang pengalaman yang berhubungan dengan
pancaindera, seperti apa bentuknya, suaranya, rasanya. Kebanyakan teks
deskriptif memang tentang pengalaman visual, tapi nyatanya pengalaman
selain dari indera penglihatanpun bisa digunakan dalam descriptive text.
Namun secara khusus, descriptive text adalah, "......
is a text which says what a person or a thing is like. Its purpose is
to describe and reveal a particular person, place, or thing." [teks
yang menjelaskan gambaran seseorang atau benda. Tujuannya adalah
mengambarkan atau mengungkapkan orang, tempat atau benda tertentu]
Jadi, bisa dikatakan bahwa descriptive text ini adalah teks yang menjelaskan tentang seperti apakah orang atau suatu benda dideskripsikan, baik bentuknya, sifat-sifatnya, jumlahnya dan lain-lain. Tujuan (purpose) dari descriptive text pun jelas, yaitu untuk menjelaskan, MENGGAMBARKAN atau mengungkapkan seseorang atau suatu benda.
Jadi, bisa dikatakan bahwa descriptive text ini adalah teks yang menjelaskan tentang seperti apakah orang atau suatu benda dideskripsikan, baik bentuknya, sifat-sifatnya, jumlahnya dan lain-lain. Tujuan (purpose) dari descriptive text pun jelas, yaitu untuk menjelaskan, MENGGAMBARKAN atau mengungkapkan seseorang atau suatu benda.
Generic Structure dalam Descriptive Text
Ketika menulis descriptive text, ada beberapa susunan umum / generic structure (sebenarnya tidak wajib) agar tulisan kita dianggap benar. Susunan tersebut adalah :
- Identification : berisi tentang identifikasi hal / seorang yang akan dideskripsikan.
- Description : berisi tentang penjelasan / penggambaran tentang hal / seseorang dengan menyebutkan beberapa sifatnya.
Ketika kita
menulis descriptive text, hal yang wajib kita ketahui adalah cara kita
menyampaikan deskripsi tulisan kita tersebut. Oleh karena itu pemahaman
tentang adjective (kata sifat bahasa Inggris) wajib kita kuasai.
Selain
adjective, beberapa struktur bahasa Inggris yang berfungsi sebagai
adjective pun harus kita pahami agar penulisan descriptive text kita
terlihat tidak kaku.
Contoh Descriptive Text tenang Ibu
My mother is a beautiful person. She is not tall but not
short, and she has curly hair and brown. Her eyes color are like honey
and her color skin color light brown, and she has a beautiful
smile. Her weight likes 120 lbs.
She is a very kind person. She is very lovely, friendly, patient, and she loves to help people. I love my mom, because she is a good example to me. She loves being in the Church, and she loves sing and dance too.
She is a very good child, wife and mother. She always takes care of her family. She likes her house to be clean and organized. She a very organized person, and all things in the house are in the right place. She doesn't like messes.
She always has a smile on her face. She is so sweet and lovely. I like when I am going to sleep or went I wake up or when I am going to go to some places, she always give me a kiss, and when the family have a problem she always be with us to helps us and to give us all her love.
She is a very kind person. She is very lovely, friendly, patient, and she loves to help people. I love my mom, because she is a good example to me. She loves being in the Church, and she loves sing and dance too.
She is a very good child, wife and mother. She always takes care of her family. She likes her house to be clean and organized. She a very organized person, and all things in the house are in the right place. She doesn't like messes.
She always has a smile on her face. She is so sweet and lovely. I like when I am going to sleep or went I wake up or when I am going to go to some places, she always give me a kiss, and when the family have a problem she always be with us to helps us and to give us all her love.
Kamis, 05 April 2012
Jumat, 16 Maret 2012
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