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Trigonometry
Memory Aid
To know Sin Angle = opp
Hyp
Oh
Hell
Cos Angle = adj
Hyp
Another
Hour
Tan Angle= opp
Adj
Of
Algebra
Opp=opposite side to angle
Adj =adjacent side to angle
Hyp= hypotenuse =opposite
the right angle/slanted side
Use Sin, Cos, Tan and Pythagoras Theorem for right angled triangles
Use cos to find x as you have the hyp and you want adj to the angle
Cos Angle = adj
Hyp
cos 60° =
x
10
x = 10(cos 60°)
x = 5
pick Tan to solve because you have the opp and the adj to the angle
Tan Angle= opp
Adj
Tan A =
4
4
A = tan−1 1
A = 45°
use 2ndf Tan(Tan-1) to get the angle
Pythagoras theorem
H
h2=a2+b2
A
hyp2 = other 2 sides squared
hyp is always the slanted side the one opposite the box or right angle
b
Example
X is an acute angle such that the Sin X = ½. Find the Cos X?
Draw out triangle 1st and put in the opp=1 and hyp=2 to the angle X.
1
h2=a2+b2
2
22 = 12 +b2
4 = 1 + b2
4-1 = b2
3 = b2
√3 = b
X
b
Cos X = adj
hyp
=
√3
2
Also Tan X = opp = 1
adj √3
Example of Pythagoras theorem
hyp is always opposite right angle
x2 = 82 + 62
Get x 1st
x2 = 64 + 36
x2 = 100
Square root 100 to get rid of square
x = 10
262 = 102 + y2
when you get x sub back in to find y
y2 = 576
Square root 576 to get rid of square
y = 24