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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. Pythagorean trigonometric identity - Wikipedia

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

    The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity involving the cotangent and the cosecant also follows from the Pythagorean theorem.

  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. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    if γ is obtuse, and so cos γ is negative, then −ab cos γ is the area of the parallelogram with sides a and b forming an angle of γ′ = γ − ⁠ π / 2 ⁠. Acute case. Figure 7a shows a heptagon cut into smaller pieces (in two different ways) to yield a proof of the law of cosines.

  6. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The accuracy of the approximations can be seen below in Figure 1 and Figure 2. As the measure of the angle approaches zero, the difference between the approximation and the original function also approaches 0.

  7. 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 ...

  8. My Top 10 Stocks to Buy in 2024 Are Beating the Market by 48% ...

    www.aol.com/top-10-stocks-buy-2024-211100857.html

    An equal investment in an S&P 500 index fund would be worth $12,890. For example, when the S&P 500 lost 18% in 2022, 51% of U.S. equity managers underperformed the market. My Top 10 Stocks to Buy ...

  9. Trigonometric tables - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_tables

    Historically, the earliest method by which trigonometric tables were computed, and probably the most common until the advent of computers, was to repeatedly apply the half-angle and angle-addition trigonometric identities starting from a known value (such as sin(π/2) = 1, cos(π/2) = 0).