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8. Trig and Matlab

8. Trig and Matlab - Trigonometry and Matlab Trig you...

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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
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©2009 by L. Lagerstrom Trig You Should Know You should be well-versed 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, triangle-based 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.)
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©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
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©2009 by L. Lagerstrom Trig You Should Know, cont. You should know (or know how to figure out quickly): • Often-used 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 30-60-90 and 45-45-90 triangles. • The law of sines and the law of cosines for a non-right 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 = = α cos 2 2 2 2 bc c b a - + =
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Matlab code Command window display ©2009 by L. Lagerstrom Sine, Cosine, and Tangent in Matlab %The three basic trig functions in %Matlab are sin, cos, and tan. (There
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