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  2. List of trigonometric identities - Wikipedia

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

    Historically, the first four of these were known as Werner's formulas, after Johannes Werner who used them for astronomical calculations. [29] See amplitude modulation for an application of the product-to-sum formulae, and beat (acoustics) and phase detector for applications of the sum-to-product formulae.

  3. Reciprocity (photography) - Wikipedia

    en.wikipedia.org/wiki/Reciprocity_(photography)

    For example, for a given film, if a light meter indicates a required EV of 5 and the photographer sets the aperture to f/11, then ordinarily a 4-second exposure would be required; a reciprocity correction factor of 1.5 would require the exposure to be extended to 6 seconds for the same result. Reciprocity failure generally becomes significant ...

  4. Proofs of trigonometric identities - Wikipedia

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

    For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number, except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°). Referring to the diagram at the right, the six ...

  5. Real image - Wikipedia

    en.wikipedia.org/wiki/Real_image

    In other words, a real image is an image which is located in the plane of convergence for the light rays that originate from a given object. Examples of real images include the image produced on a detector in the rear of a camera, and the image produced on an eyeball retina (the camera and eye focus light through an internal convex lens).

  6. 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.

  7. 30 Color Photos Photographers Took 100 Years Ago That Still ...

    www.aol.com/44-old-color-photos-showing...

    Image credits: Detroit Photograph Company Even though the autochrome was patented in 1903, that doesn't mean that it was readily available to the public. "Only affluent amateur photographers were ...

  8. Pythagorean trigonometric identity - Wikipedia

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

    By the periodicity identities we can say if the formula is true for −π < θ ≤ π then it is true for all real θ. Next we prove the identity in the range ⁠ π / 2 ⁠ < θ ≤ π. To do this we let t = θ − ⁠ π / 2 ⁠, t will now be in the range 0 < t ≤ π/2. We can then make use of squared versions of some basic shift identities ...

  9. Savings interest rates today: Give thanks for savings with ...

    www.aol.com/finance/savings-interest-rates-today...

    The FDIC is an independent government agency charged with maintaining stability and public confidence in the U.S. financial system and providing insurance on consumer deposit accounts.