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2. Law of sines - Wikipedia

   en.wikipedia.org/wiki/Law_of_sines

   In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, ⁡ = ⁡ = ⁡ =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.

3. Exact trigonometric values - Wikipedia

   en.wikipedia.org/wiki/Exact_trigonometric_values

   In mathematics, the values of the trigonometric functions can be expressed approximately, as in ⁡ (/), or exactly, as in ⁡ (/) = /.While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots.

4. Mnemonics in trigonometry - Wikipedia

   en.wikipedia.org/wiki/Mnemonics_in_trigonometry

   Signs of trigonometric functions in each quadrant. All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. 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. Trigonometry - Wikipedia

   en.wikipedia.org/wiki/Trigonometry

   The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to "co-". [32] With these functions, one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines. [33]

6. Proofs of trigonometric identities - Wikipedia

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

   For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. 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°).

7. Sine and cosine - Wikipedia

   en.wikipedia.org/wiki/Sine_and_cosine

   In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...