# Trigonometry

for most questions arc and sector area are measured in readians (unless specified)
Just remember:

TO CONVERT
divide by (pi) and the multiply by 180
(pi)/4 ------> 45

divide by 180, multiply by (Pi)
60 --------> (Pi)/3

ANGLES TO REMEMBER

DEGREES     0             30             45             60             90             120             180             270             360        RADIANS   0     (Pi)/6    (Pi)/4   (Pi)/6   (Pi)/2   (2Pi)/3       Pi      (3Pi)/2     2Pi

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## Arc Length and sector length

ARC LENGTH

S=r(Theta)

S=r(theta) where r=10cm and (Theta)=0.7
S= 10 X 0.7
S= 7cm

SECTOR AREA

A=1/2( r^2 X Theta)

A= 1/2( r^2 X Theta) where r=10cm and (Theta)= 0.7
A= 1/2 ( 10^2 X 0.7)
A= 1/2 (70)
A= 35cm^2

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## Trig Formulas

SIN RULE (2 angles and 1 side)
a/SINA = b/SINB = c/SINC

COSINE RULE ( 3 sides or an angle between two sides)
a^2= b^2 + c^2 - 2bcCosA

AREA OF A TRIANGLE
A= 1/2 abSinC

PROOFS OF TRIG FUNCTIONS

Tan(x) = Sin(x)/Cos(x)

(Sin(x))^2 + (Cos(x))^2 =1

proofs come up a lot in exams so you will need to know these. you may be given some formula and have to manipulate it in order to get it to look like either of these.

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## Graphs of trig functions

SIN AND COS GRAPHS ARE ALWAYS IN THE RANGE OF -1 TO 1

SIN GOES THROUGH THE ORIGIN

COS CROSSES AT 1

TAN IS ALL OVER THE FLIPPING PLACE. IT STRETCHES FROM - INFINITY TO INFINITY IN THE Y AND CROSSES X EVERY 180 DEGREES

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## Solving trig equations at given intervals

USING GRAPHS
find the range that you want and draw a line for y=Cosx
where the line crosses the graph you have your points

USING CAST
this is a diagram that looks like a cartesian graph but has the letters C A S T anticlockwise starting from the bottom right quadrant
now put in the first angle and start working all the angles out

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