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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...

   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 θ < θ. So we have ⁡ < <. For negative values of θ we have, by the symmetry of the sine function

4. Tangent half-angle substitution - Wikipedia

   en.wikipedia.org/wiki/Tangent_half-angle...

   As t goes from 0 to 1, the point follows the part of the circle in the first quadrant from (1, 0) to (0, 1). Finally, as t goes from 1 to +∞, the point follows the part of the circle in the second quadrant from (0, 1) to (−1, 0). Here is another geometric point of view. Draw the unit circle, and let P be the point (−1, 0).

5. Small-angle approximation - Wikipedia

   en.wikipedia.org/wiki/Small-angle_approximation

   [1] [2] One reason for this is that they can greatly simplify differential equations that do not need to be answered with absolute precision. 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.

6. Trigonometric substitution - Wikipedia

   en.wikipedia.org/wiki/Trigonometric_substitution

   Trigonometric identities may help simplify the answer. [ 1 ] [ 2 ] Like other methods of integration by substitution, when evaluating a definite integral, it may be simpler to completely deduce the antiderivative before applying the boundaries of integration.

7. ID Protection by AOL

   help.aol.com/articles/id-protection-by-aol

   Around the clock protection: MyReputation Discovery ® provides 24-hour monitoring for mentions of your address, phone number, or other information on the web. ID Protection by AOL works around the clock to help secure your identity, usernames, passwords and personal information. With the amount of data being stolen and exposed by criminals and ...