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  2. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.

  3. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    Using the squeeze theorem, [4] we can prove that ⁡ =, which is a formal restatement of the approximation ⁡ for small values of θ. A more careful application of the squeeze theorem proves that lim θ → 0 tan ⁡ ( θ ) θ = 1 , {\displaystyle \lim _{\theta \to 0}{\frac {\tan(\theta )}{\theta }}=1,} from which we conclude that tan ⁡ ( θ ...

  4. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    The unit circle centered at the origin in the Euclidean plane is defined by the equation: [2] x 2 + y 2 = 1. {\displaystyle x^{2}+y^{2}=1.} Given an angle θ , there is a unique point P on the unit circle at an anticlockwise angle of θ from the x -axis, and the x - and y -coordinates of P are: [ 3 ]

  5. Integration using Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Integration_using_Euler's...

    In integral calculus, Euler's formula for complex numbers may be used to evaluate integrals involving trigonometric functions.Using Euler's formula, any trigonometric function may be written in terms of complex exponential functions, namely and and then integrated.

  6. The publication notes that predicting the weather is not an exact science, but, in general, most of the U.S. is experiencing a warmer, wetter winter, and only a few spots can expect snow.

  7. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    The tangent half-angle substitution relates an angle to the slope of a line. Introducing a new variable = ⁡, sines and cosines can be expressed as rational functions of , and can be expressed as the product of and a rational function of , as follows: ⁡ = +, ⁡ = +, = +.

  8. Swiss flag concerns over Trump's US tariff hike proposals - AOL

    www.aol.com/news/swiss-raise-concerns-trumps...

    Switzerland said on Tuesday it was concerned by U.S. President-elect Donald Trump's proposals to raise tariffs and is considering how to respond if his new administration does so. Trump aims to ...

  9. The Zombie Tide are alive! Alabama has inside track to CFP ...

    www.aol.com/sports/zombie-tide-back-alabama...

    The Crimson Tide were left for dead after their third loss of the season in Week 13. Now, if things shake out right this weekend, they're in the College Football Playoff field.