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  2. List of trigonometric identities - Wikipedia

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

    Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.

  3. 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 ...

  4. Pythagorean trigonometric identity - Wikipedia

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

    Point P has a positive y-coordinate, and sin θ = sin(π−θ) > 0. As θ increases from zero to the full circle θ = 2π, the sine and cosine change signs in the various quadrants to keep x and y with the correct signs. The figure shows how the sign of the sine function varies as the angle changes quadrant.

  5. Law of sines - Wikipedia

    en.wikipedia.org/wiki/Law_of_sines

    In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, ⁡ = ⁡ = ⁡ =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.

  6. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    The order may be switched, as in "Tommy On A Ship Of His Caught A Herring" (tangent, sine, cosine) or "The Old Army Colonel And His Son Often Hiccup" (tangent, cosine, sine) or "Come And Have Some Oranges Help To Overcome Amnesia" (cosine, sine, tangent). [2] [3] Communities in Chinese circles may choose to remember it as TOA-CAH-SOH, which ...

  7. The 85 best sitewide sales to shop during Cyber Monday - AOL

    www.aol.com/lifestyle/the-best-sitewide-sales-to...

    Disney+ and Hulu bundle: $2.99 for a year. HBO Max: $2.99 for 6 months. Paramount+: 76% off for a year. Peacock: 25% off for a year. Walmart: Lowest prices of the year on headphones, TVs ...

  8. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes sin ⁡ ( 30 ∘ ) = 1 / 2 {\displaystyle \sin(30^{\circ ...

  9. Denzel Washington Has Been Sober for 10 Years, Says He ... - AOL

    www.aol.com/entertainment/denzel-washington...

    Denzel Washington revealed to Esquire magazine as part of a recent cover story that he is 10 years sober. He cut off alcohol at 60 years old after a 15-year drinking pattern that started in the ...

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