Trigonometry Notes to know for AS and A2.

Trigonometry Notes to know for AS and A2.

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Maths Alevel: Trigonometry
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Graphs of sec x, cosec x, cot x
You will also need to know the graphs and properties of the
reciprocal functions:
The following properties apply to any reciprocal function:
1. The reciprocal of zero is +
2. The reciprocal of + is zero
3. The reciprocal of 1 is 1
4. The reciprocal of 1 is 1
5. Where the function has a maximum value, its reciprocal has a
minimum value
6. If a function increases, the reciprocal decreases
7. A function and its reciprocal have the same sign
The curves of cosec x, sec x and cot x are shown below:

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From a right angled triangle we know that:
cos2 + sin2 = 1
It can also be shown that:
1 + tan2 = sec2 and cot2 + 1 = cosec2
(Try dividing the second expression by cos2 to get the first rearrangement,
and separately divide cos2 + sin2 = 1, by sin2 to get the other formula.)
These are Trigonometric Identities and useful for rewriting equations
so that they can be solved, integrated, simplified etc.…read more

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A + B) = cos A cos B sin A sin B
cos (A B) = cos A cos B + sin A sin B
Remember: take care with the signs when using these formulae.
Double angle formulae
The compound angle formulae can also be used with two equal angles
i.e. A = B.…read more

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Factor formulae
The formulae we have met so far involve manipulating single expressions
of sin x and cos x. If we wish to add sin or cos expressions together
we need to use the factor formulae, which are derived from the
compound angle rules we met earlier.…read more

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Write 5 sin x + 12 cos x in the form R cos ( )
R cos ( ) = R (cos cos + sin sin )
By matching this expansion to the question we get:
R cos cos = 12 cos and R sin sin = 5 sin
This gives:
R cos = 12 and R sin = 5
By illustrating this with a rightangled triangle, we get,
Therefore: = 22.6 o
Therefore: 5 sin + 12 cos = 13 cos( 22.…read more



A really well presented revision sheet covering all tri identities, graphs and worked examples.

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