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  2. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    When the direction of a Euclidean vector is represented by an angle , this is the angle determined by the free vector (starting at the origin) and the positive -unit vector. The same concept may also be applied to lines in a Euclidean space, where the angle is that determined by a parallel to the given line through the origin and the positive x ...

  3. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    There are a number of ways to demonstrate the validity of the small-angle approximations. The most direct method is to truncate the Maclaurin series for each of the trigonometric functions. Depending on the order of the approximation , cos ⁡ θ {\displaystyle \textstyle \cos \theta } is approximated as either 1 {\displaystyle 1} or as 11 ...

  4. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    In contrast, by the Lindemann–Weierstrass theorem, the sine or cosine of any non-zero algebraic number is always transcendental. [4] The real part of any root of unity is a trigonometric number. By Niven's theorem, the only rational trigonometric numbers are 0, 1, −1, 1/2, and −1/2. [5]

  5. Pythagorean trigonometric identity - Wikipedia

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

    Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.

  6. 6 of the best and 6 of the worst Christmas movies on Netflix ...

    www.aol.com/6-best-6-worst-christmas-120901378.html

    The holiday season is incomplete for many people without holiday movies. This year, Netflix is streaming a wide range of Christmas classics and original movies.

  7. BYD on track to top 2024 sales goal and outsell Ford, Honda - AOL

    www.aol.com/news/byd-track-top-2024-sales...

    As of last month, BYD's share of the Chinese auto market, which makes up more than 90% of its total sales, stood at 17.1%, up from 12.5% in 2023, according to data from the China Passenger Car ...

  8. Tangent half-angle substitution - Wikipedia

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

    As t goes from 0 to 1, the point follows the part of the circle in the first quadrant from (1, 0) to (0, 1). Finally, as t goes from 1 to +∞, the point follows the part of the circle in the second quadrant from (0, 1) to (−1, 0). Here is another geometric point of view. Draw the unit circle, and let P be the point (−1, 0).

  9. 'Embodiment of evil': Texas man sentenced for exploiting ...

    www.aol.com/embodiment-evil-texas-man-sentenced...

    A Houston man was sentenced to 30 years in prison after pleading guilty to sexually exploiting a 9-year-old and being a dark web administrator for a website that consisted of child sex abuse ...