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  2. List of trigonometric identities - Wikipedia

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

    Terms with infinitely many sine factors would necessarily be equal to zero. When only finitely many of the angles are nonzero then only finitely many of the terms on the right side are nonzero because all but finitely many sine factors vanish. Furthermore, in each term all but finitely many of the cosine factors are unity.

  3. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    In contrast, by the Lindemann–Weierstrass theorem, the sine or cosine of any non-zero algebraic number is always transcendental. [4] The real part of any root of unity is a trigonometric number. By Niven's theorem, the only rational trigonometric numbers are 0, 1, −1, 1/2, and −1/2. [5]

  4. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    The y-axis ordinates of A, B and D are sin θ, tan θ and csc θ, respectively, while the x-axis abscissas of A, C and E are cos θ, cot θ and sec θ, respectively. Signs of trigonometric functions in each quadrant. Mnemonics like "all students take calculus" indicates when sine, cosine, and tangent are positive from quadrants I to IV. [8]

  5. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4. [ 5 ] Quadrant 1 (angles from 0 to 90 degrees, or 0 to π/2 radians): All trigonometric functions are positive in this quadrant.

  6. Proofs of trigonometric identities - Wikipedia

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

    The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...

  7. Tangential angle - Wikipedia

    en.wikipedia.org/wiki/Tangential_angle

    In this case, the curvature κ is given by φ′(s), where κ is taken to be positive if the curve bends to the left and negative if the curve bends to the right. [1] Conversely, the tangent angle at a given point equals the definite integral of curvature up to that point: [4] [1]

  8. Pythagorean trigonometric identity - Wikipedia

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

    Point P has a positive y-coordinate, and sin θ = sin(π − θ) > 0. As θ increases from zero to the full circle θ = 2π, the sine and cosine change signs in the various quadrants to keep x and y with the correct signs. The figure shows how the sign of the sine function varies as the angle changes quadrant.

  9. Quadrant (plane geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadrant_(plane_geometry)

    Signs of trigonometric functions in each quadrant. In the above graphic, the words in quotation marks are a mnemonic for remembering which three trigonometric functions (sine, cosine, tangent and their reciprocals) are positive in each quadrant. The expression reads "All Science Teachers Crazy" and proceeding counterclockwise from the upper ...