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  "body": "\n## Definition\n\nLet $\\sin, \\cos \\colon \\R \\to \\R$ be the [[sine and cosine|0WB57D9488]] functions, given by their power series.\nLet $Z_{\\cos} = \\set{x \\in \\R : \\cos x = 0}$ and $Z_{\\sin} = \\set{x \\in \\R : \\sin x = 0}$.\nThe *trigonometric functions* are $\\sin$, $\\cos$, and the four functions\n$$\\tan x = \\frac{\\sin x}{\\cos x}, \\quad \\sec x = \\frac{1}{\\cos x} \\quad (x \\in \\R \\setminus Z_{\\cos}),$$\n$$\\cot x = \\frac{\\cos x}{\\sin x}, \\quad \\csc x = \\frac{1}{\\sin x} \\quad (x \\in \\R \\setminus Z_{\\sin}).$$\nThey are called tangent, secant, cotangent and cosecant.\n\n## Remarks\n\nHere $Z_{\\cos} = \\set{\\pi/2 + k\\pi : k \\in \\Z}$ and $Z_{\\sin} = \\set{k\\pi : k \\in \\Z}$.\n\nExample: $x = \\pi/3$ lies in neither set, and $\\sin(\\pi/3) = \\sqrt3/2$, $\\cos(\\pi/3) = 1/2$, so $\\tan(\\pi/3) = \\sqrt3$, $\\sec(\\pi/3) = 2$, $\\cot(\\pi/3) = 1/\\sqrt3$ and $\\csc(\\pi/3) = 2/\\sqrt3$.\n\nNon-example of a value: $\\tan(\\pi/2)$ is not defined, because $\\cos(\\pi/2) = 0$, so $\\pi/2 \\in Z_{\\cos}$; the tangent tends to $+\\infty$ as $x \\to \\pi/2$ from the left.\n\nThe functions $\\sin$, $\\cos$, $\\sec$ and $\\csc$ have period $2\\pi$, and $\\tan$ and $\\cot$ have period $\\pi$.\nThe [[tangent function|06T0HS14PP]] has its own node.\n",
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