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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.
Then multiplying the numerator and denominator inside the square root by (1 + cos θ) and using Pythagorean identities leads to: = + . Also, if the numerator and denominator are both multiplied by (1 - cos θ), the result is:
Take a hyperbolic plane whose Gaussian curvature is .Given a hyperbolic triangle with angles ,, and side lengths =, =, and =, the following two rules hold.The first is an analogue of Euclidean law of cosines, expressing the length of one side in terms of the other two and the angle between the latter:
Earlier this week, the organization stated that despite some calls to roll up the red carpet, it was determined to keep the Oscars on track for Sunday, March 2, at the Dolby Theatre in Hollywood.
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A major shakeup is coming to The View!. The long-running daytime talk show announced it would add a 30-minute weekend slot to its coverage called The Weekend View starting Saturday, Jan. 11 ...
NEW YORK - "Save the Last Dance" was released on January 12, 2001. Almost 24 years to the day, the film's star Julia Stiles is back in theaters, albeit in a different fashion. Stiles makes her ...
The following is a list of integrals (antiderivative functions) of trigonometric functions.For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions.