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  2. List of trigonometric identities - Wikipedia

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

    The half-angle formula for sine can be obtained by replacing with / and taking the square-root of both sides: ⁡ (/) = (⁡) /. Note that this figure also illustrates, in the vertical line segment E B ¯ {\displaystyle {\overline {EB}}} , that sin ⁡ 2 θ = 2 sin ⁡ θ cos ⁡ θ {\displaystyle \sin 2\theta =2\sin \theta \cos \theta } .

  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. Proofs of trigonometric identities - Wikipedia

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

    Then multiplying the numerator and denominator inside the square root by (1 + cos θ) and using Pythagorean identities leads to: ⁡ = ⁡ + ⁡. Also, if the numerator and denominator are both multiplied by (1 - cos θ), the result is:

  5. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    Write a 1 in the middle where the three triangles touch; Write the functions without "co" on the three left outer vertices (from top to bottom: sine, tangent, secant) Write the co-functions on the corresponding three right outer vertices (cosine, cotangent, cosecant) Starting at any vertex of the resulting hexagon:

  6. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.

  7. 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.

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