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  2. 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:

  3. Pythagorean trigonometric identity - Wikipedia

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

    satisfying respectively y(0) = 0, y′(0) = 1 and y(0) = 1, y′(0) = 0. It follows from the theory of ordinary differential equations that the first solution, sine, has the second, cosine, as its derivative, and it follows from this that the derivative of cosine is the negative of the sine. The identity is equivalent to the assertion that the ...

  4. 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.

  5. Law of tangents - Wikipedia

    en.wikipedia.org/wiki/Law_of_tangents

    In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a, b, and c are the lengths of the three sides of the triangle, and α, β, and γ are the angles opposite those three respective

  6. Dick Van Dyke Gathers 'Big Family' at Home Ahead of 99th ...

    www.aol.com/dick-van-dyke-gathers-big-133000649.html

    PEOPLE is exclusively premiering Coldplay's extended directors’ cut music video for "All My Love" The video stars Dick Van Dyke, who reflects on his career ahead of his 99th birthday on Dec. 13

  7. Ford to cut European jobs as EV shift, Chinese rivals take toll

    www.aol.com/news/ford-cut-14-european-jobs...

    Shares in Ford were down 1.8% following news of the measures, which will be a big blow in particular for Germany, where Europe's bigg Ford to cut European jobs as EV shift, Chinese rivals take ...

  8. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = ⁡ (″) and the above approximation follows when tan X is replaced by X.

  9. Big 12 fines Arizona State $25,000 for premature field storm ...

    www.aol.com/sports/big-12-fines-arizona-state...

    Arizona State has been fined for the chaotic end to its win over BYU on Saturday. The Big 12 said Tuesday that it was fining the school $25,000 and issuing a public reprimand for the field storm ...