Library/Algebra/Trigonometry/Trigonometry (other)

Trigonometry (other)

Overview
Important

Beyond basic trigonometric ratios and identities, trigonometry includes advanced concepts such as the Law of Sines, Law of Cosines, sum and difference formulas, and solving trigonometric equations. These tools help solve problems involving triangles that are not right-angled and analyze more complex relationships between angles and sides.

Important properties

  • Law of Sines: Relates the sides and angles of any triangle: asin⁡A=bsin⁡B=csin⁡C\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}.

  • Law of Cosines: Generalizes the Pythagorean theorem: c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos C.

  • Sum and difference formulas: For example, sin⁡(A±B)=sin⁡Acos⁡B±cos⁡Asin⁡B\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B.

  • Trigonometric equations can have multiple solutions within a given interval.