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  2. Proofs of trigonometric identities - Wikipedia

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

    This geometric argument relies on definitions of arc length and area, which act as assumptions, so it is rather a condition imposed in construction of trigonometric functions than a provable property. [2] For the sine function, we can handle other values. If θ > π /2, then θ > 1. But sin θ ≤ 1 (because of the Pythagorean identity), so sin ...

  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 1 − 1 ...

  4. 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.

  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. "I [thought to myself], ‘Oh, no, this is not going to happen today,’ ” Linda Rosa recalled of the incident

  7. Ohio Woman, 75, Killed and Partially Eaten by Neighbor ... - AOL

    www.aol.com/ohio-woman-75-killed-partially...

    When police entered the residence at approximately 3 p.m. they found a large pig inside, per WBNS. The Dispatch reported that police believe Westergaard Rigney was attacked by two pigs “roaming ...

  8. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

  9. NYC woman murdered 33 years ago finally ID’d as ... - AOL

    www.aol.com/nyc-woman-murdered-33-years...

    One of them pleaded guilty in September of 1992 to first-degree manslaughter and was sentenced to 8 1/3 to 25 years in jail. He was cut loose in 2009 on parole, which discharged him in August of 2016.