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Core 2: Trigonometry. Key formulae and ideas
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Cosine
Rule
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There are 3
sides involved, a, b &c There is an
angle, A, which is opposite side a
OR
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Finding a
side, x. We can use
the cosine rule because we KNOW TWO SIDES and the side we want is OPPOSITE
the angles
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Finding a
missing angle. Notice how
we KNOW THREE SIDES, so we can use the cosine-rule.
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Sine-Rule
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Or
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Observe how
the angles and sides are opposite each other. This means we can use the
sine-rule.
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Call missing
angle x.
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This is an
interesting problem. We want to
find p, but we do not have an opposite side! However, if
we call the other missing angle x, then:
So to find p, we do: |
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Radians
and degrees Radians and
degrees are two different scales for measuring angles. There is a
direct relationship between the two of them which makes it easy to convert
between the two of them.
In other
words |
To convert
from degrees to radians we:
Example:
To convert
from radians to degrees we:
Examples:
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Radians
allow some properties of curved shapes to be worked out particularly quickly. Arc and
Sectors
This sector
is a fraction of a circle. The angle is
measured in radians.
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KEY FORMULA FOR
A SECTOR
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Basic
problem: Find area and perimeter
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Angle
already given in radians so:
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More
challenging problem: A sector has
an area of 5 The sector
also has an arc length of 3.4 Find |
Solution Turn the
information into equations
Observe the trick:
So,
So,
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