![](\"resources/question-resources/exact_values_radians_We6EFEi.svg\")
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 $\\dfrac{\\pi}{3}$.
\n
Alternatively, 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
The exact value of $\\csc\\Large($$\\var{distheta}\\Large)$ is
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