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By drawing the following triangles we can determine the exact values of $\\sin$, $\\cos$ and $\\tan$ (and their reciprocals $\\csc$, $\\sec$, $\\cot$) for the angles $30^\\circ$, $45^\\circ$ and $60^\\circ$.
\nAlternatively, one can memorise the following table:
\n\n\n | $30^\\circ$ | \n$45^\\circ$ | \n$60^\\circ$ | \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
The exact value of $\\sin(\\var{theta}^\\circ)$ is
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