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The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, P 2 (cos θ) = 0, and so any interaction which depends on this second-order Legendre polynomial vanishes at the magic angle.
[2] [6] [verification needed] [better source needed] Thus the user might measure a block of metal and come away with a width of 208.92 mm when the true width is 208.91 mm, a difference that matters to the subsequent machining.
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.
Elon Musk hints at bringing back Vine. Days before Yusupov's announcement, Elon Musk, Tesla CEO and SpaceX founder, was tagged in an X post that included Vine's logo with the caption, "I think it ...
President Volodymyr Zelenskiy said on Tuesday his team spoke with U.S. President Donald Trump's national security adviser and his top envoy on the war in Ukraine this week, and that they were ...
The updated prediction comes after additional observations, and weeks of back and forth. On Feb. 18, NASA scientists predicted a 3.1% chance of the asteroid hitting our planet on Dec. 22, 2032.
Signs of trigonometric functions in each quadrant. All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4.
[27] [28] Using the Taylor series approximations of sine and cosine, he produced a sine table to 12 decimal places of accuracy and a cosine table to 9 decimal places of accuracy. He also gave the power series of π and the angle , radius , diameter , and circumference of a circle in terms of trigonometric functions.