“우리 대부분은 초라한 옷차림과 엉터리 가구들을 부끄럽게 여기지만, 초라한 생각과 엉터리 철학을 부끄럽게 여길 줄 알아야 한다.” – Albert Einstein

19900103
trigonometry laws and identities

https://www.eeweb.com/tools/trigonometry-laws-and-identities-sheet

Law of Sines

latex!encoded:base64,XGZyYWN7c2luXGFscGhhfXtcYWxwaGF9ID0gXGZyYWN7c2luIFxiZXRhfXtifT1cZnJhY3tzaW4gXGdhbW1hfXtjfQ==

Law of Cosines

latex!encoded:base64,YV57Mn0gPWJeezJ9ICtjXnsyfSAtMmJj
latex!encoded:base64,Y29zIFxhbHBoYQ==
latex!encoded:base64,Yl57Mn0gPWFeezJ9ICtjXnsyfSAtMmFj
latex!encoded:base64,Y29zIFxiZXRh
latex!encoded:base64,Y157Mn0gPWFeezJ9ICtiXnsyfSAtMmFi
latex!encoded:base64,Y29zIFxnYW1tYQ==

Law of Tangents

latex!encoded:base64,XGZyYWN7YS1ifXthK2J9ID0gXGZyYWN7dGFuW1xmcmFjezF9ezJ9KFxhbHBoYSAtIFxiZXRhKV19e3RhbltcZnJhY3sxfXsyfShcYWxwaGEgKyBcYmV0YSldfQ==
latex!encoded:base64,XGZyYWN7Yi1jfXtiK2N9ID0gXGZyYWN7dGFuW1xmcmFjezF9ezJ9KFxiZXRhIC0gXGdhbW1hKV19e3RhbltcZnJhY3sxfXsyfShcYmV0YSArIFxnYW1tYSldfQ==
latex!encoded:base64,XGZyYWN7YS1jfXthK2N9ID0gXGZyYWN7dGFuW1xmcmFjezF9ezJ9KFxhbHBoYSAtIFxnYW1tYSldfXt0YW5bXGZyYWN7MX17Mn0oXGFscGhhICsgXGdhbW1hKV19

Mollweid’s Formula

latex!encoded:base64,XGZyYWN7YStifXtjfSA9IFxmcmFje2Nvc1tcZnJhY3sxfXsyfSAoXGFscGhhIC0gXGJldGEpIF19IHtzaW4oXGZyYWN7MX17Mn0pIFxnYW1tYX0=

Trig Identities Math Help

Tangent and Cotangent Identities

latex!encoded:base64,dGFuXHRoZXRhID0gXGZyYWN7c2luXHRoZXRhfSB7Y29zXHRoZXRhfQ==
latex!encoded:base64,Y290XHRoZXRhID0gXGZyYWN7Y29zXHRoZXRhfXtzaW5cdGhldGF9

Reciprocal Identities

latex!encoded:base64,Y3NjXHRoZXRhID0gXGZyYWN7MX17c2luXHRoZXRhfQ==
latex!encoded:base64,c2VjXHRoZXRhID0gXGZyYWN7MX17Y29zXHRoZXRhfQ==
latex!encoded:base64,Y290XHRoZXRhID0gXGZyYWN7MX17dGFuXHRoZXRhfQ==
latex!encoded:base64,c2luXHRoZXRhID0gXGZyYWN7MX17Y3NjXHRoZXRhfQ==
latex!encoded:base64,Y29zXHRoZXRhID0gXGZyYWN7MX17c2VjXHRoZXRhfQ==
latex!encoded:base64,dGFuXHRoZXRhID0gIFxmcmFjezF9e2NvdFx0aGV0YX0=

Pythagorean Identities

latex!encoded:base64,c2luXnsyfVx0aGV0YSArIGNvc157Mn1cdGhldGEgPSAx
latex!encoded:base64,dGFuXnsyfVx0aGV0YSArIDEgPSBzZWNeezJ9XHRoZXRh
latex!encoded:base64,Y290XnsyfVx0aGV0YSArIDEgPWNzY157Mn1cdGhldGE=

Even and Odd Identities

latex!encoded:base64,c2luKC0gXHRoZXRhKSA9IC1zaW5cdGhldGE=
latex!encoded:base64,Y29zKC1cdGhldGEpID0gY29zXHRoZXRh
latex!encoded:base64,dGFuKC1cdGhldGEpID0gLXRhblx0aGV0YQ==
latex!encoded:base64,Y3NjKC1cdGhldGEpID0gLWNzY1x0aGV0YQ==
latex!encoded:base64,c2VjKC1cdGhldGEpID0gc2VjXHRoZXRh
latex!encoded:base64,Y290KC1cdGhldGEpID0gLWNvdFx0aGV0YQ==

Periodic Identities

latex!encoded:base64,c2luKFx0aGV0YSArIDJccGkgbiApID0gc2luXHRoZXRh
latex!encoded:base64,Y29zKFx0aGV0YSArIDJccGkgbikgPSBjb3NcdGhldGE=
latex!encoded:base64,dGFuKFx0aGV0YSArIFxwaSBuKSA9IHRhblx0aGV0YQ==
latex!encoded:base64,Y3NjKFx0aGV0YSArIDJccGkgbikgPSBjc2NcdGhldGE=
latex!encoded:base64,c2VjKFx0aGV0YSArIDJccGkgbikgPSBzZWNcdGhldGE=
latex!encoded:base64,Y290KFx0aGV0YSArIFxwaSBuKSA9IGNvdFx0aGV0YQ==

Double Angle Identities

latex!encoded:base64,c2luKDJcdGhldGEpID0gMiBzaW5cdGhldGEgY29zXHRoZXRh
latex!encoded:base64,Y29zKDJcdGhldGEpID0gY29zXnsyfVx0aGV0YSAtc2luXnsyfVx0aGV0YQ==
latex!encoded:base64,PTIgY29zXnsyfVx0aGV0YSAtMQ==
latex!encoded:base64,PTEgLTJzaW5eezJ9XHRoZXRh
latex!encoded:base64,dGFuKDIgXHRoZXRhKSA9IFxmcmFjezJ0YW5cdGhldGF9ezEtdGFuXnsyfVx0aGV0YX0=

Half Angle Identities

latex!encoded:base64,c2luIFxsZWZ0IChcZnJhY3tcdGhldGF9ezJ9IFxyaWdodCkgPSBccG1cc3FydHtcZnJhY3sxLWNvc1x0aGV0YX17Mn19
latex!encoded:base64,Y29zIFxsZWZ0IChcZnJhY3tcdGhldGF9ezJ9IFxyaWdodCkgPSBccG0gXHNxcnR7XGZyYWN7MStjb3NcdGhldGF9ezJ9fQ==
latex!encoded:base64,dGFuIFxsZWZ0IChcZnJhY3tcdGhldGF9ezJ9IFxyaWdodCkgPSBccG0gXHNxcnR7XGZyYWN7MS1jb3NcdGhldGF9ezErY29zXHRoZXRhfX0=

Sum and Difference Identities

latex!encoded:base64,c2luKFxhbHBoYSBccG0gXGJldGEpID0gc2luIFxhbHBoYSBjb3MgXGJldGEgXHBtIGNvcyBcYWxwaGEgc2luIFxiZXRh
latex!encoded:base64,Y29zKFxhbHBoYSBccG0gXGJldGEpID0gY29zIFxhbHBoYSBjb3MgXGJldGEgXG1wIHNpbiBcYWxwaGEgc2luIFxiZXRh
latex!encoded:base64,dGFuKFxhbHBoYSBccG0gXGJldGEpID0gXGZyYWN7dGFuIFxhbHBoYSBccG0gdGFuIFxiZXRhfXsgMSBcbXAgdGFuIFxhbHBoYSB0YW4gXGJldGF9

Product to Sum Identities

latex!encoded:base64,c2luIFxhbHBoYSBzaW4gXGJldGEgPSBcZnJhY3sxfXsyfVtjb3MoXGFscGhhLVxiZXRhKSAtIGNvcyhcYWxwaGEgKyBcYmV0YSld
latex!encoded:base64,Y29zIFxhbHBoYSBjb3MgXGJldGEgPSBcZnJhY3sxfXsyfSBbY29zKFxhbHBoYSAtIFxiZXRhKSArIGNvcyhcYWxwaGEgK1xiZXRhKV0=
latex!encoded:base64,c2luIFxhbHBoYSBjb3MgXGJldGEgPSBcZnJhY3sxfXsyfVtzaW4oXGFscGhhICtcYmV0YSkgKyBzaW4gKFxhbHBoYSAtIFxiZXRhKV0=
latex!encoded:base64,Y29zIFxhbHBoYSBzaW4gXGJldGEgPSBcZnJhY3sxfXsyfVtzaW4gKFxhbHBoYSArIFxiZXRhKSAtc2luIChcYWxwaGEgLVxiZXRhKV0=

Sum to Product Identities

latex!encoded:base64,c2luIFxhbHBoYSArIHNpbiBcYmV0YSA9IDIgc2luIFxsZWZ0ICggXGZyYWN7XGFscGhhK1xiZXRhfXsyfSBccmlnaHQpIGNvcyBcbGVmdCggXGZyYWN7XGFscGhhIC1cYmV0YX17Mn1ccmlnaHQp
latex!encoded:base64,c2luIFxhbHBoYSAtIHNpbiBcYmV0YSA9IDIgY29zXGxlZnQgKFxmcmFje1xhbHBoYSArIFxiZXRhfXsyfVxyaWdodCkgc2luIFxsZWZ0KFxmcmFje1xhbHBoYS1cYmV0YX17Mn1ccmlnaHQp
latex!encoded:base64,Y29zXGFscGhhICsgY29zIFxiZXRhID0gMiBjb3MgXGxlZnQoXGZyYWN7XGFscGhhK1xiZXRhfXsyfVxyaWdodCkgY29zXGxlZnQoXGZyYWN7XGFscGhhLVxiZXRhfXsyfVxyaWdodCk=
latex!encoded:base64,Y29zXGFscGhhIC0gY29zIFxiZXRhID0gLTIgc2luIFxsZWZ0KFxmcmFje1xhbHBoYStcYmV0YX17Mn1ccmlnaHQpIHNpblxsZWZ0KFxmcmFje1xhbHBoYS1cYmV0YX17Mn1ccmlnaHQp

Cofunction Identities

latex!encoded:base64,c2luIFxsZWZ0KFxmcmFje1xwaX17Mn0tXHRoZXRhXHJpZ2h0KSA9IGNvc1x0aGV0YQ==
latex!encoded:base64,Y29zXGxlZnQoXGZyYWN7XHBpfXsyfS1cdGhldGFccmlnaHQpID0gIHNpblx0aGV0YQ==
latex!encoded:base64,dGFuXGxlZnQoXGZyYWN7XHBpfXsyfS1cdGhldGFccmlnaHQpID0gIGNvdFx0aGV0YQ==
latex!encoded:base64,Y3NjXGxlZnQoXGZyYWN7XHBpfXsyfS1cdGhldGFccmlnaHQpID0gIHNlY1x0aGV0YQ==
latex!encoded:base64,c2VjXGxlZnQoXGZyYWN7XHBpfXsyfS1cdGhldGFccmlnaHQpID0gIGNzY1x0aGV0YQ==
latex!encoded:base64,Y290XGxlZnQoXGZyYWN7XHBpfXsyfS1cdGhldGFccmlnaHQpID0gIHRhblx0aGV0YQ==

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