Download Trigonometry

Trigonometry – Intro
(from the Greek trigonon = three angles and metro = measure)
trigonometry is for right angle triangles only
using trigonometry:
given the angle and a side length,
we can determine another side length
given two side lengths,
we can determine the angle
hypotenuse
opposite (side to angle a)
a
adjacent (side to angle a)
hypotenuse – the side opposite the right angle (opposite the 90º angle),
– it is also always the longest side of a right-angled triangle.
opposite – the side opposite to the angle we are interested in (angle a).
adjacent – the side that is in next to the angle we are interested in (angle a)
and next to the right angle
Trigonometry Functions:
Sine (short form: sin)
Cosine (short form: cos)
Tangent (short form: tan)
Sine
the sine of an angle, is the ratio of
the length of the opposite side to the length of the hypotenuse
opposite
sin( angle ) 
hypotenuse
Cosine
the cosine of an angle, is the ratio of
the length of the adjacent side to the length of the hypotenuse
adjacent
cos(angle ) 
hypotenuse
Tangent
the tangent of an angle, is the ratio of
the length of the opposite side to the length of the adjacent side
opposite
tan( angle ) 
adjacent
SOH CAH TOA – how to remember the trig ratios…
SOH
CAH
TOA
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent
Trigonometry – Intro
Identifying the: hypotenuse, the opposite side, the adjacent side
opposite
hypotenuse
(to angle a)
hypotenuse
opposite
(to angle a)
adjacent
a
adjacent
(to angle a)
(to angle a)
a
adjacent
adjacent
(to angle a)
(to angle a)
a
a
opposite
hypotenuse
(to angle a)
opposite
a
a
adjacent
hypotenuse
hypotenuse
(to angle a)
(to angle a)
hypotenuse
adjacent
(to angle a)
opposite
opposite
(to angle a)
(to angle a)
opposite
opposite
(to angle a)
(to angle a)
adjacent
hypotenuse
(to angle a)
a
adjacent
(to angle a)
hypotenuse
a
Trigonometry – Intro
Finding a side length, when given the angle and another side length
n?
3
opposite
hypotenuse
sin( 37º ) 
0.6018 
0.6018 3

1
n
3
n
0.6018n = 3
37º
n=5
therefore, the hypotenuse = 5
5
adjacent
hypotenuse
cos(37º ) 
0.7986 
n
5
0.7986 n

1
5
1n = 3.993
37º
n=4
n?
therefore, the adjacent side = 4
tan( 37º ) 
n?
opposite
adjacent
0.7535 
n
4
0.7535 n

1
4
1n = 3.014
n=3
37º
therefore, the opposite side = 3
4
Finding the angle, when given 2 side lengths
5
3
sin( a ) 
opposite
hypotenuse
sin( a ) 
3
5
a?
sin( a )  0.6
a = 37º
therefore, angle a = 37º
cos(a ) 
5
adjacent
hypotenuse
cos(a ) 
4
5
a?
a = 37º
therefore, angle a = 37º
4
3
a?
cos(a )  0.8
tan( a ) 
opposite
adjacent
tan( a ) 
3
4
tan( a )  0.75
a = 37º
therefore, angle a = 37º
4