# If cot(theta)=7, what is sin(theta), cos(theta), sec(theta) between 0 and 2 pi?

If $\mathrm{cot}\left(\theta \right)=7$, what is $\mathrm{sin}\left(\theta \right),\mathrm{cos}\left(\theta \right),\mathrm{sec}\left(\theta \right)$ between 0 and $2\pi$?
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averes8

Draw a right-angled triangle ABC where B is 90 deg, A is $\theta .\mathrm{cot}\left(\theta \right)=A\frac{B}{B}C=7.AC=\sqrt{{7}^{2}+1}=5\sqrt{2}.AB=7,BC=1.$
$\mathrm{sin}\left(\theta \right)=B\frac{C}{A}C=\frac{1}{5}\sqrt{2}=0.2\frac{\sqrt{2}}{2}=0.1\sqrt{2}=0.1414.$
$\mathrm{cos}\left(\theta \right)=\frac{7}{5}\sqrt{2}=1.4\frac{\sqrt{2}}{2}=0.7\sqrt{2}=0.9899.$
$\mathrm{sec}\left(\theta \right)=\frac{1}{\mathrm{cos}\left(\theta \right)}=5\frac{\sqrt{2}}{7}=1.0102$. These are all approximate values and apply to quadrant 1. $\mathrm{cot}\left(\theta \right)=\frac{7}{1}$ in quadrant 1, or $-\frac{7}{-1}$ in quadrant 3. In this quadrant sin, cos, sec are all negative, so $\mathrm{sin}\left(\theta \right)=-0.1414,\mathrm{cos}\left(\theta \right)=-0.9899,\mathrm{sec}\left(\theta \right)=-1.0102$ in QIII, and 0.1414, 0.9899, 1.0102 in QI.