$\mathrm{sin}\theta =-\frac{1}{4}$, Quadrant IV

opinaj
2022-09-30
Answered

A function value and a quadrant are given. Find the other five function values.

$\mathrm{sin}\theta =-\frac{1}{4}$, Quadrant IV

$\mathrm{sin}\theta =-\frac{1}{4}$, Quadrant IV

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Lamar Esparza

Answered 2022-10-01
Author has **8** answers

$\mathrm{sin}\theta =-\frac{1}{4}$, Quadrant IV

In Quadrant IV only $\mathrm{cos}\theta $ and $\mathrm{sec}\theta $ are fue

$\mathrm{cos}\theta =\sqrt{1-{\mathrm{sin}}^{2}\theta}\phantom{\rule{0ex}{0ex}}=\sqrt{1-\frac{1}{16}}\phantom{\rule{0ex}{0ex}}=\frac{\sqrt{15}}{4}$

$\mathrm{tan}\theta =\frac{\frac{-1}{4}}{\frac{\sqrt{15}}{4}}\phantom{\rule{0ex}{0ex}}=\frac{-1}{\sqrt{15}}$

In Quadrant IV only $\mathrm{cos}\theta $ and $\mathrm{sec}\theta $ are fue

$\mathrm{cos}\theta =\sqrt{1-{\mathrm{sin}}^{2}\theta}\phantom{\rule{0ex}{0ex}}=\sqrt{1-\frac{1}{16}}\phantom{\rule{0ex}{0ex}}=\frac{\sqrt{15}}{4}$

$\mathrm{tan}\theta =\frac{\frac{-1}{4}}{\frac{\sqrt{15}}{4}}\phantom{\rule{0ex}{0ex}}=\frac{-1}{\sqrt{15}}$

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