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Core 2: Trigonometry. Key formulae and ideas
Cosine
Rule

There are 3
sides involved, a, b &c There is an
angle, A, which is opposite side a OR 


Finding a
side, x. We can use
the cosine rule because we KNOW TWO SIDES and the side we want is OPPOSITE
the angles 


Finding a
missing angle. Notice how
we KNOW THREE SIDES, so we can use the cosinerule. [the side opposite the angle] 
SineRule 
Or 


Observe how
the angles and sides are opposite each other. This means we can use the
sinerule. 

Call missing
angle x.

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: 
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: 

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. denotes the radius of the circle 
KEY FORMULA FOR
A SECTOR 

Basic
problem: Find area and perimeter

Angle
already given in radians so: 

More
challenging problem: A sector has
an area of 5 The sector
also has an arc length of 3.4 Find and 
Solution Turn the
information into equations Observe the trick: So, So, 