This is the third book in the series that included 'The Theory of Nothing' the "The Universe Revealed.' My purpose in this new book is to more fully explain how science is actually done and how science fits into our culture along with religion and p...
@Baekternity asked for a discourse on how circular functions are used in science.
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First of all, circular functions are also more familiarly known as trigonometric functions. You know, sine, cosine and tangent. The reason why they're called circular functions is that they involve angles around a circle.
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One such use in physics involves converting vector coordinates into Cartesian coordinates and visa versa. A vector is a directional value that has both length and direction. A Cartesian coordinate of a vector is given as the x, y values.
A vector can be given in polar coordinates or in Cartesian coordinates. For example a polar coordinate is given as x = r x sin (θ) where r is the length of the vector and θ is the angle of the vector A Cartesian coordinate is given as x and y.
To convert from polar to Cartesian one uses r = √ (x2 + y2) (the square root of x squared plus y squared).
To convert from Cartesian to polar one uses x = r x cos(θ) and y = r x sin (θ)
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Here is how trig functions are used in physics: A projectile is fired into the air at 35 degrees at 120 meters/sec. Find the Cartesian coordinates of the projectile. y = (120 m/s) x (sin (35)) = 69 m/s x = (120 m/s) x (cos (35)) = 98 m/s 69 squared plus 98 squared equals 120 squared, which is the original speed.
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Another use of trig in physics is when trying to calculate work when the force is not directed in a straight line. W = F s cos (x) where F is force, s is the displacement of the force (the distance). And x is the angle of the direction of the force.
These are only three simple ways in which so-called circular functions are used in physics. However, they are two of the most important ones.
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