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Trigononometry
The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.
(according to dictionary.com)
The CAST rule tells you which function is positive in each quadrant
2
3
1
4
SOH
Sine = Opposite/Hypotenuse
CAH
Cosine = Adjacent/Hypotenuse
TOA
Tangent = Opposite/Adjacent
Reference Angle
Reference Angle
To find a side:
1
2
a²=((b²+c²)- (2bc cosA))
THE SINE LAW
SinA SinB SinC
____ = ____ = ____
a b c
a b c
____ = ____ = ____
SinA SinB SinC
An equation relating the lengths of the sides of any shaped triangle to the sines of its angles
Ambiguous Cases
4
3
C
a
b
= Standard Angle
s
180°
B
A
= Reference Angle
c
R
150°
To find an angle:
cosA = (b²+c²-a²/2bc)
30°
180°-150°=30°
B
*Use angles to find exact values
"Count To Three"
(60°)
30°-60°-90°
Isosceles
a
Sin30° = 1/2
Cos30° = 3/2
Tan30° = 1/ 3
Sin45° = 1/ 2
Cos45° = 1/ 2
Tan45° = 1
c
Finding Exact Values Using Angles
(90°)
(30°)
C
A
Sin60° = 3/2
Cos60° = 1/2
Tan60° = 3
b
'A' is usually used as the reference angle
B
(45°)
45° - 45° - 90°
a
c
2
1
(90°)
(45°)
C
A
b