Maths - Pythagoras, Trigonometry, Surds

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  • Created by: Alice
  • Created on: 02-05-13 16:11

How to label a Triangle

(http://blog.shortfusion.com/supporting/circulartext/triangle.gif)Hypotenuse - Always the longest side

Oppostite - Always oppsite to angle (not right angle)    Adjacent - side of angle

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Phythagoras

Right-angled triangles

Pythagoras' Theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides'. (The hypotenuse is the longest side and it's always opposite the right angle)

So for any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Pythagoras only works for right angled triangles

http://www.bbc.co.uk/schools/gcsebitesize/maths/videos/pythagoras_video1.shtml

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Pythagoras - Equation

The equation is:

(http://ncalculators.com/images/pythagoras-theorem.gif)

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Trigonometry - Formulae

The three formulae: sin, cos, tan

There are three formulae involved in trigonometry:

sinopposite / hypotenuse

cosadjacent / hypotenuse

tanopposite / adjacent

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How to use Trigonometry

(http://www.foundation-flash.com/tutorials/anglesandlengths/trigeasy1.png)

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How to use Trigonometry

1) Label the sides that you have the pieces of data on . If you use the triangle before, the sides labled would be the Hypotenuse and the Opposite

2) Now you know this data, use SOH CAH TOA to work out which formula you need. Inn this case, you would use Sin (SOH) because you have the Opposite and the hypotenuse. 

3) You then need to plug the numbers you have into the equation

E.g. Sin60 = Opp / Hyp

4) You then type this equation into the calculator and you should get the answer

http://www.bbc.co.uk/schools/gcsebitesize/maths/videos/trigonometry_video1.shtml

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Surds

  • A surd is a square root which cannot be reduced to a whole number. For example,square root of 4 = 2 (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/surdsrev2_1.png) is not a surd, as the answer is a whole number. But square root of 5 (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/surdsrev2_3.png) is not a whole number. 

Rules:

square root of ab = square root of a x square root of b (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/surdsrev2_4.png)

square root of a x square root of a = a (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/surdsrev2_5.png)

If you have a squared number you need to split it up into 2 number that times into the original number and sqaure them. 

http://www.bbc.co.uk/schools/gcsebitesize/maths/videos/surds_video1.shtml

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Rationalize Surds

Rationalising an expression means getting rid of any surds from the bottom of fractions. 

http://www.bbc.co.uk/schools/gcsebitesize/maths/number/surdsrev1.shtml

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