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Recall that $\\csc\\theta=\\dfrac{1}{\\sin\\theta}$, $\\sec\\theta=\\dfrac{1}{\\cos\\theta}$, and $\\cot\\theta=\\dfrac{1}{\\tan\\theta}$.

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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 $\\dfrac{\\pi}{6}$, $\\dfrac{\\pi}{4}$ and $\\dfrac{\\pi}{3}$.

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Alternatively, one can memorise the following table: 

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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\dfrac{\\pi}{6}$$\\dfrac{\\pi}{4}$$\\dfrac{\\pi}{3}$
 
$\\sin$$\\dfrac{1}{2}$$\\dfrac{1}{\\sqrt{2}}$$\\dfrac{\\sqrt{3}}{2}$
 
$\\cos$$\\dfrac{\\sqrt{3}}{2}$$\\dfrac{1}{\\sqrt{2}}$$\\dfrac{1}{2}$
 
$\\tan$$\\dfrac{1}{\\sqrt{3}}$$1$$\\sqrt{3}$
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Often we prefer to work with exact values rather than approximations from a calculator.

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$2$

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$\\sqrt{2}$

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$\\dfrac{2}{\\sqrt{3}}$

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$\\sqrt{3}$

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$\\dfrac{1}{\\sqrt{3}}$

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$1$

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The exact value of $\\csc\\Large($$\\var{distheta}\\Large)$ is

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$2$

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$\\sqrt{2}$

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$\\dfrac{2}{\\sqrt{3}}$

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$\\sqrt{3}$

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$\\dfrac{1}{\\sqrt{3}}$

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$1$

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The exact value of $\\sec\\Large($$\\var{distheta}\\Large)$ is

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$2$

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$\\sqrt{2}$

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$\\dfrac{2}{\\sqrt{3}}$

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$\\sqrt{3}$

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$\\dfrac{1}{\\sqrt{3}}$

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$1$

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The exact value of $\\cot\\Large($$\\var{distheta}\\Large)$ is

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multiple choice testing csc, sec, cot  of  random(pi/6, pi/4, pi/3) radians

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'\\$\\\\frac{\\pi}{6}\\$'

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