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Recall that $\\csc\\theta=\\dfrac{1}{\\sin\\theta}$, $\\sec\\theta=\\dfrac{1}{\\cos\\theta}$, and $\\cot\\theta=\\dfrac{1}{\\tan\\theta}$.
\n\nBy drawing the following triangles we can determine the exact values of $\\sin$, $\\cos$ and $\\tan$ (and their reciprocals $\\csc$, $\\sec$, $\\cot$) for the angles $\\dfrac{\\pi}{6}$, $\\dfrac{\\pi}{4}$ and $\\dfrac{\\pi}{3}$.
\nAlternatively, one can memorise the following table:
\n\n\n | $\\dfrac{\\pi}{6}$ | \n$\\dfrac{\\pi}{4}$ | \n$\\dfrac{\\pi}{3}$ | \n
\n | \n | \n | \n |
$\\sin$ | \n$\\dfrac{1}{2}$ | \n$\\dfrac{1}{\\sqrt{2}}$ | \n$\\dfrac{\\sqrt{3}}{2}$ | \n
\n | \n | \n | \n |
$\\cos$ | \n$\\dfrac{\\sqrt{3}}{2}$ | \n$\\dfrac{1}{\\sqrt{2}}$ | \n$\\dfrac{1}{2}$ | \n
\n | \n | \n | \n |
$\\tan$ | \n$\\dfrac{1}{\\sqrt{3}}$ | \n$1$ | \n$\\sqrt{3}$ | \n
Often we prefer to work with exact values rather than approximations from a calculator.
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