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©2009 by L. Lagerstrom
Trigonometry and Matlab
• Trig you should know
• Sine, cosine, and tangent in Matlab
• Inverse trig functions and quadrant restrictions
• The atan2 function
©2009 by L. Lagerstrom
Trig You Should Know
You should be wellversed in basic trigonometric concepts by now
in your math and science career. In particular for this course, it is
expected that you know:
• The geometric, trianglebased definitions of sine, cosine, and
tangent on the unit circle (diagram on next slide).
• That sine, cosine, and tangent are pure, dimensionless numbers
(literally, ratios of the sides of a right triangle with given angles).
Because we use them so often, it's easy to forget this (especially
that they don't have units associated with them!).
• That angles may be measured in degrees or radians, and that
the relationship between them is 360 degrees = 2
π
radians.
(Think of the unit circle: its circumference is 2
π
, corresponding to
360 degrees around.) So to convert degrees to radians, multiply
by
π
/180. Or multiply by 180/
π
to convert from radians to degrees.
(It helps to remember that an angle's value in radians is always a
smaller number than its value in degrees.)
©2009 by L. Lagerstrom
Trig You Should Know, cont.
The unit circle and trig definitions are shown. The angles are
given in radians. Note the labeling of the quadrants (
I, II, III, IV
).
x
y
r = 1
θ
(x=1,y=0),
θ
= 0
(x=0,y=1),
θ
=
π
/2
(x=1,y=0),
θ
=
π
= 
π
(x=0,y=1),
θ
= 
π
/2
sin
θ
= y/r,
y = rsin
θ
cos
θ
= x/r,
x = rcos
θ
tan
θ
= y/x
I
II
III
IV
©2009 by L. Lagerstrom
Trig You Should Know, cont.
You should know (or know how to figure out quickly):
• Oftenused angles in radians: 30 degrees =
π
/6 radians, 45
degrees =
π
/4 radians, 60 degrees =
π
/3 radians, 90 degrees =
π
/2
radians, and their multiples.
• Sine, cosine, and tangent values for 306090 and 454590
triangles.
• The law of sines and the law of cosines for a nonright triangle with
sides a, b, and c and angles
α
,
β
, and
γ
opposite each corresponding
side, respectively:
Law of sines:
Law of cosines:
(and similar variations starting with b
2
or c
2
)
c
b
a
γ
β
α
sin
sin
sin
=
=
cos
2
2
2
2
bc
c
b
a

+
=