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  2. List of trigonometric identities - Wikipedia

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

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  3. Proofs of trigonometric identities - Wikipedia

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

    For the tan function, the equation is: tan ⁡ θ 2 = ± 1 − cos ⁡ θ 1 + cos ⁡ θ . {\displaystyle \tan {\frac {\theta }{2}}=\pm \,{\sqrt {\frac {1-\cos \theta }{1+\cos \theta }}}.} Then multiplying the numerator and denominator inside the square root by (1 + cos θ) and using Pythagorean identities leads to:

  4. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    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 2 θ 2 {\textstyle 1-{\frac {1}{2}}\theta ^{2}} .

  5. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    In the integral , we may use = ⁡, = ⁡, = ⁡. Then, = ⁡ ⁡ = ⁡ (⁡) = ⁡ ⁡ = = + = ⁡ +. The above step requires that > and ⁡ > We can choose to be the principal root of , and impose the restriction / < < / by using the inverse sine function.

  6. Tangent half-angle substitution - Wikipedia

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

    The tangent of half an angle is important in spherical trigonometry and was sometimes known in the 17th century as the half tangent or semi-tangent. [2] Leonhard Euler used it to evaluate the integral ∫ d x / ( a + b cos ⁡ x ) {\textstyle \int dx/(a+b\cos x)} in his 1768 integral calculus textbook , [ 3 ] and Adrien-Marie Legendre described ...

  7. Testing forgotten rape kits could free the innocent. Here’s ...

    www.aol.com/testing-forgotten-rape-kits-could...

    After nine years and nearly $350 million, USA TODAY confirmed just one exoneration resulting from a grant program to address untested rape kits.

  8. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    The fixed point iteration x n+1 = cos(x n) with initial value x 0 = −1 converges to the Dottie number. Zero is the only real fixed point of the sine function; in other words the only intersection of the sine function and the identity function is sin ⁡ ( 0 ) = 0 {\displaystyle \sin(0)=0} .

  9. 'One Tree Hill' co-star says he wanted to date Bethany Joy ...

    www.aol.com/one-tree-hill-costar-says-165336730.html

    A "One Tree Hill" love story that wasn't: Tyler Hilton revealed he once tried to date co-star Bethany Joy Lenz but her cult got in the way.