Trigonometry Math facts

 Trigonometry Math facts:

What is sine used for in trigonometry

Use sine ratio to calculate angles and sides (Sin = o/h )

One of the trigonometric ratios is the sine ratio. It is the opposite side over the hypotenuse of right triangles. In other words, we can find the angles and sides of right-angled triangles by using the sine ratios.

What is sin cos tan?

Sin is equal to the side opposite the angle that you are conducting the functions on over the hypotenuse which is the longest side in the triangle. Cos is adjacent over the hypotenuse. And tan is opposite over adjacent, which means tan is sin/cos. This can be proved with some basic algebra.

 

Why Sine is called sine 

The word "sine" (Latin "sinus") comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, 

 

Names of triangles:

"There are four types of triangle: equilateral, isosceles, scalene, and right-angled." Fleur said: "There are only three types of triangle. These are equilateral, isosceles and scalene.

 

Pythagoras therum 

- a² + b² = c²

1. Input the two lengths that you have into the formula. For example, suppose you know a = 4, b = 8 and we want to find the length of the hypotenuse c.
2. After the values are put into the formula we have 4²+ 8² = c²
3. Square each term to get 16 + 64 = c²
4. Combine like terms to get 80 = c²
5. Take the square root of both sides of the equation to get c = 8.94. Go ahead and check it with our Pythagorean theorem calculator!

Sine - Soh - opp/hyp

Cosine - Cah - adj/hyp

Tangent - Toa - opp/adj

 

Square root:  Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.

 

 

 

Saw horse assessment

Manufacture of a Saw Horse using Hand tools for my Building Construction  Industry Trades Organization qualification.

In term 1 2021 I learned how to use hand tools to manufacture a Saw Horse to a specific size from a set of drawings. This took about 6 weeks (24 hrs) I will explain how to make a sawhorse in this blog post

Here is my finished project.

This project was made by using hand tools only. No powered tools were used apart from a battery-powered drill to drill the holes for the screws.

I enjoyed measuring  the most because it taught me not to measure under the mark we needed because some people have mucked their sawhorse up because they didn't mark and measure it right 

I found cutting the most difficult part. I overcame this by practicing with some of the offcuts out of the scrap box

In this assessment, these tools are required to make a sawhorse.

- Tenon saw

- engineered square

- pencil

- ruler

- Sliding bevel

- marking gauge

- hand plane

- copping saw

To make a sawhorse I carried out the following processes.

• Marking out the top.

• Cutting the joints

• Hand sewing the leg ends.

• Marking out / planing the legs

• Fixing the legs

• Attaching the end piece and support.

Do you think you could make one?

The freedom writers

The freedom writers

the past two days we have been watching the freedom writers for our film study.  In the movie, I focused on making a change and if you put in the effort you can do what you want.

What I really liked about this movie is that Ms. G the Teacher helped the kids change their life and that the fact she was having trobles at home and had other people trying to pull her down such as the VP ( Vice Principal) she tried to get what she believed in. She made a huge impact on the class 203s. When she first started she had no recourses because the kids were 'Dumb" and that's the "couldn't read" she went out of her way and picked up a couple more shifts at a different job so she could found the class new books to read and Diaries. At the start of the movie when she first becomes a teacher no of the students liked her because she was a new teacher but by the end of the movie they didn't want to leave the classroom.

Ms. G wanted to find out what their life was like and to see what their personal lives were like so she brought some diaries for every student and if they wanted to share them with the teacher they would put them in a locked cupboard.

With them writing in there diaries the students started liking the teacher because he made her class fun and made them learn in a way that they got the most information but they didn't know, there was a scene where they were all dancing in the classroom that made me think of how they were experiencing what love felt like it but they didn't realize because they were having such fun they were all getting along and they could be there selfs

Mean Median mode

Who invented median?

-Francis Galton 

Who invented mode?

-Karl Pearson 

Who invented Mean?

- The term is first found in the mid-1690s in the writings of Edmund Halley.

What does Median mean?

- The middle value of a range of values.

What does Mode mean?

- The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.

What does Mean mean?

- The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

Why do we use Median?

- The mean value of numerical data is without a doubt the most commonly used statistical measure. Sometimes the median is used as an alternative to the mean. ... Just like the mean value, the median also represents the location of a set of numerical data by means of a single number.

Why do we use Mode?

- Mode is most useful as a measure of central tendency when examining categorical data, such as models of cars or flavors of soda, for which a mathematical average median value based on ordering can not be calculated.

Why do we use Mean?

-  The mean can be used to get an overall idea, or picture, of the data set. Mean is best used for a data set with numbers that are close together. The median can be used to get an idea of what values fall above the midpoint and what values fall below the midpoint.

These links are where I got my information on

mean

median

mode

My Pepeha and culture

Ko Richard tōku pāpā. (father)

Ko Tracey tōku māmā. (mother)

Ko Jack tōku ingoa. (your name)

Nō Christchurch ahau. (where you are from)

Ko Bluff hill tōku maunga (your mountain). 

Ko Te Huruhuru Ao o Horomaka tōku kura. (Hornby High is my school)

How to work out the volume?

 

How to work out the volume?

What do we mean by volume?

- the amount of space that a substance or object occupies or that is enclosed within a container.

How do we measure it?

- In math, the volume is the amount of space in a certain 3D object. For example, a fish tank has 3 feet in length, 1 foot in width, and two feet in height. To find the volume, you multiply length times width times height, which is 3x1x2, which equals six. So the volume of the fish tank is 6 cubic feet.

Is there a conversion to liters?

- A liter is a cubic decimetre, which is the volume of a cube 10 centimeters × 10 centimeters × 10 centimeters (1 L ≡ 1 dm3 ≡ 1000 cm3). Hence 1 L ≡ 0.001 m3 ≡ 1000 cm3 and 1 m3 (i.e. a cubic meter, which is the SI unit for volume) is exactly 1000 L.

The volume of a rectangle

- To find the volume of a rectangle, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

The volume of a cylinder

- A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r²

The volume of a prism 

-Volume of a rectangular prism = (length x width x height) cubic units. V = (l x w x h) cubic units

The volume of a barrel

- Formula. Barrel Volume = πh12 (2D² + d²

The volume of a cone

There is a kiddy pool in the back garden it is 3 meters wide 8 meters long and we can only fill it 1.2m high.

- How much water does it take to full?

to calculate I use 

lxbxh

3 x 8 x l.2 = 28.8

I know that 1m3 = 1 liter = 1000cm3

28.8 x 1000 = 28800 liter

-the pool is on a deck how heavy is it?

3m x 8m x 1.2m = 28.8M3

1l = 1kg

28.8 x 1000 = 28800kg

There is a trailer of barrels 

Each barrel is 1.5m high with a diameter of 0.75m

how much weight is on the trailer

0.75/2 = 0.375

3.142 x 0.375 x 2 = 2.3565m2

2.3565 x 1000 - 2356.5

2356.5 x 6 = 14139L

M3

Cm3

Mm3

Tom Gate evolution

 

Text title: Tom Gates Genius idea

Text type: book  

Text creator: Liv Pichon

Text purpose: To Read

Date: 3, March 2021

The brilliant Tom Gates is back in this, the fourth installment of this award-winning series from Liz Pichon. In this volume of his hilarious diary, Tom documents the ups and downs of his daily life as he deals everything from Dad's embarrassing new fitness regime to the challenges of entering his band DOGZOMBIES into the school Talent Contest - and most horrifying of all, seeing weirdo big sister Delia without her sunglasses.

Both existing fans of Tom Gates and newcomers to the series will be delighted by this wickedly funny and engaging story. With plenty of Tom's scribbly illustrations, doodles, and lively hand-drawn cartoons throughout, as well as a fun flipbook, it is an appealingly visual read that will keep young readers entertained from beginning to end.

Area of basic shapes

Today in maths we are learning about the area of basic shapes.

The area can be defined as the space occupied by a flat shape or the surface of an object.

- Rectangle

the area is measured with the formula w x h 

w = width

h = Height

- Circle

The area of a circle is measured with a formula PI x R2 

Circumference = 2 x pi x r

r = Radius

PI = 22/7 or 3.141

- Triangle

The area of a circle is measured with a formula 1/2 x b x h

b = base

h = verticle height  

Circles

How do I calc the circumference of a circle? Formular based

Using radiance

Circumference 2 PI Radius

Using diameter PI Diameter

 

These are the units of calculating a circle.

PI = 22/7

What is the perimeter or circumference of the circles?

- Diameter = 40 meters

- Radius = 20 meters

- PI = 22/7 or 3.141

To calc the perimeter or circumference of the circles I can use 2 PI Radius or PI Diameter.

Cir = 2 x 3.141 x 20 m

= 125.66 meters

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------

Radius - 15 meters

PI = 22/7 or 3.141

To calc the perimeter or circumference of the circles I can use 2 PI Radius or PI Diameter.

Cir 2x 3.141 x 15m

= 94.28m

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------

Diameter = 22.5 meters

Radius 11.25 meter

PI = 22/7 or 3.141

To calc the perimeter or the circumference, I am going to use PIdeiamter

Cir 3.141 x 22.5m

= 70.71 meter

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------

Radius = 26cm

Diameter = 52 cm 

PI = 22/7 or 3.141

To convert the radius from cm to M I am going to divide it by 100

Radius

26

------- = 0.26m

100

Diameter

52

------- = 0.52m

100

To calc the perimeter of the circumference, I am doing to use 2PI x r

Cir 2 x  PI x 0.26m 

= 1.63362817987m

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------

Radius = 26000mm

Diameter = 520000

PI = 22/7 or 3.141

To convert the radius from cm to M I am going to divide it by 100

26000

------------ = 260 m

100

Cir 2 x PI x 260

=1633.62817987

Converting mm to km chart

 

mm	cm	m	km
12000mm	1200cm	12m	0.012
5000mm	500cm	5m	0.005km
12000000mm	120000cm	1200m	1.2km
326mm	32.6cm	3.26m	0.00326
1200mm	120cm	1.2m	0.0012

5 Common tools in a workshop

Carpenter pencils:

Carpenter pencils are created to be rectangle so then when they are put down on an angled surface they don't roll away

Marking blade:

A marking blade is a handle with a blade at the end. you use a marking blade when you don't have a pencil or if you prefer the indent.

Sliding bevel:

A sliding bevel is an adjustable gauge that used for setting and transferring a 90-degree angle

Rip saw:

A rip saw, or tooth saw, is an all-purpose tool for woodworking when you want to make rough cuts. 

Chisel:

A chisel is used for carving or cutting a hard material such as wood, stone, or metal by hand, struck with a mallet 

Timber- VOT

Explain the different parts of a tree

Trees have three main parts - the leaves, the trunk, and the roots. The upper part of the tree with the branches is called the crown.

Outer bark

The outer bark is the tree's protection from the outside world. Continually renewed from within, it helps keep out moisture in the rain and prevents the tree from losing moisture when the air is dry. It insulates against cold and heat and wards off insect enemies.

 

Phloem

Phloem transports carbohydrates, produced by photosynthesis and hydrolysis of reserve compounds, to sink tissues for growth, respiration, and storage. At photosynthetic tissues, carbohydrates are loaded into the phloem.

 

Cambium

The cambium cell layer is the growing part of the trunk. It annually produces new bark and new wood in response to hormones that pass down through the phloem with food from the leaves. These hormones, called “auxins”, stimulate growth in cells.

Xylem

Xylem, plant vascular tissue that conveys water and dissolved minerals from the roots to the rest of the plant and also provides physical support. Xylem tissue consists of a variety of specialized, water-conducting cells known as tracheary elements.

Heartwood

The heartwood functions as long-term storage of biochemicals, which vary from species to species. These chemicals are known collectively as extractives.

Describe how trees become timber.

The trees get cut to a set length Then the log gets picked up by a timber lorry, which transports the timber to a processing site such as, sawmill, paper mill, pallet fencing, or construction producer, AT the chosen site the log gets debarked or bucked, Drys out, Cut to length than dressed.

Sorce

This is the site where I got my info

Outer bark

Phloem

Cambium

Xylem

Heartwood

Processes of timber 

Defects of tree

Defects in timber.

Defects are visible signs that a tree is failing to grow or live. These are the seven main types of tree defects dead. Wood, cracks, weak branch unions, decay, cankers, root problems, and poor tree form. These seven main types of tree defects are described below.

Different types of cut,

There are three different types of cuts in timber. Quartersaw, Riftsaw, and Plain saw

Quartersaw

- This reveals a different face for the board, giving straight grain, and the end of a board shows growth rings 60-90 degrees to the face of the board.

Riftsaw

-riftsawn wood is the least effective and most expensive means by converting a log. But it is the most stable.

Plain saw

-plain saw is just a straight cut wood. it is the most common type of cut due to it being the most inexpensive and easiest way to cut the wood.

In New Zealand, we use four main timbers Kauri, Matai, and Rewarewa, and Rimu These timbers are chosen on the basis of their colors, grain patterns, and workability, which lend them to be creatively used.