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

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    The Hoosiers are comfortably in the field, but at 11-1 they, too, don’t have a victory over a top-25 opponent and are behind two-loss teams Georgia (5th), Ohio State (6th) and Tennessee (7th).

  7. This Is The Healthiest Source Of Protein, According To A New ...

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    (The current guidance is 1.5 cups a week.) To be fair, most Americans aren’t big bean eaters , but the country's top dietitians and nutritionists are hoping to change that.

  8. The 5 best US cities to celebrate New Year's Eve, ranked - AOL

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    The personal finance website WalletHub compared 100 of the biggest US cities on entertainment, food, costs, safety, and accessibility.

  9. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    In the last step we took the reciprocals of the three positive terms, reversing the inequities. Squeeze: The curves y = 1 and y = cos θ shown in red, the curve y = sin( θ )/ θ shown in blue. We conclude that for 0 < θ < ⁠ 1 / 2 ⁠ π, the quantity sin( θ )/ θ is always less than 1 and always greater than cos(θ).