# Find the remaining trigonometric ratios using the given value: sec 0 =-1.5, (pi)/2 < 0 < pi

Find the remaining trigonometric ratios using the given value:
$\mathrm{sec}0=-1.5,\frac{\pi }{2}<0<\pi$
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kawiarkahh
$\mathrm{sin}\theta =\frac{0}{H}$
$\mathrm{cos}\theta =\frac{A}{H}$
$\mathrm{tan}\theta =\frac{0}{A}$
$\mathrm{csc}\theta =\frac{H}{0}$
$\mathrm{sec}\theta =\frac{H}{A}$
$\mathrm{cot}\theta =\frac{A}{0}$

$\mathrm{sec}\theta =-1.5$
$\mathrm{sec}\theta =\frac{-3}{2}$
$\frac{\pi }{2}<\theta \pi$

${2}^{2}-{?}^{2}={3}^{2}$
${?}^{2}=5$
$?=\sqrt{5}$
$\mathrm{sin}\theta =\frac{\sqrt{5}}{3}$
$\mathrm{cos}\theta =\frac{-2}{3}$
$\mathrm{tan}\theta =-\frac{\sqrt{5}}{2}$
$\mathrm{csc}\theta =\frac{3}{\sqrt{5}}=\frac{3\sqrt{5}}{5}$
$\mathrm{cot}\theta =\frac{2}{\sqrt{5}}=\frac{-2\sqrt{5}}{5}$
$\mathrm{sin}\theta >0$
$\mathrm{csc}\theta >0$

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Jeffrey Jordon

Answer is given below (on video)

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