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  2. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The quantity 206 265 ″ is approximately equal to the number of ... where the values for sin(0.75) and cos(0.75) are obtained from trigonometric table. The result is ...

  3. Proofs of trigonometric identities - Wikipedia

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

    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 trigonometric functions of θ are, for angles smaller than the right angle:

  4. 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.

  5. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. 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.

  6. 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} .

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  8. These states are increasing minimum coverage requirements in 2025

    www.aol.com/finance/states-increasing-minimum...

    Utah minimum coverage limits will increase to 30/60/25. Virginia limits will be 50/100/25. ... so 30 equals $30,000. These dollar amounts represent your policy limits. That means, in the event of ...

  9. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    It is even possible to obtain a result slightly greater than one for the cosine of an angle. The third formula shown is the result of solving for a in the quadratic equation a 2 − 2ab cos γ + b 2 − c 2 = 0. This equation can have 2, 1, or 0 positive solutions corresponding to the number of possible triangles given the data.