MathGoldMedalist
Sign InRegister

Toolkit 36

General Solutions of Trigonometric Equations

sin⁡α=sin⁡β  ⇒  α=β+360k,  180−β+360k,  k∈Z\sin\alpha=\sin\beta\;\Rightarrow\;\alpha=\beta+360k,\;180-\beta+360k,\;k\in\mathbb{Z}
cos⁡α=cos⁡β  ⇒  α=±β+360k,  k∈Z\cos\alpha=\cos\beta\;\Rightarrow\;\alpha=\pm\beta+360k,\;k\in\mathbb{Z}
tan⁡α=tan⁡β  ⇒  α=β+180k,  k∈Z\tan\alpha=\tan\beta\;\Rightarrow\;\alpha=\beta+180k,\;k\in\mathbb{Z}
cot⁡α=cot⁡β  ⇒  α=β+180k,  k∈Z\cot\alpha=\cot\beta\;\Rightarrow\;\alpha=\beta+180k,\;k\in\mathbb{Z}
Back to Toolkit