# A function value and a quadrant are given. Find the other five function values. sin theta=-1/4, quadrant IV

A function value and a quadrant are given. Find the other five function values.
$\mathrm{sin}\theta =-\frac{1}{4}$, Quadrant IV
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Lamar Esparza
$\mathrm{sin}\theta =-\frac{1}{4}$, Quadrant IV
In Quadrant IV only $\mathrm{cos}\theta$ and $\mathrm{sec}\theta$ are fue
$\mathrm{cos}\theta =\sqrt{1-{\mathrm{sin}}^{2}\theta }\phantom{\rule{0ex}{0ex}}=\sqrt{1-\frac{1}{16}}\phantom{\rule{0ex}{0ex}}=\frac{\sqrt{15}}{4}$
$\mathrm{tan}\theta =\frac{\frac{-1}{4}}{\frac{\sqrt{15}}{4}}\phantom{\rule{0ex}{0ex}}=\frac{-1}{\sqrt{15}}$