ordewayaeroge9sqy

2023-02-25

Find the values of the other trigonometric functions of θ from the information given $\mathrm{cos}\theta =-\frac{5}{8}$, $\mathrm{tan}\theta <0$

Ruby Rollins

Beginner2023-02-26Added 5 answers

${\mathrm{sin}}^{2}x=1-{\mathrm{cos}}^{2}x=1-\frac{25}{64}=\frac{39}{64}=0.61\to \mathrm{sin}x=0.78$

$\mathrm{tan}x=\frac{\mathrm{sin}x}{\mathrm{cos}x}=\frac{0.78}{-0.625}=-1.25$

$\mathrm{cot}x=\frac{1}{-1.25}=-0.80$

$\mathrm{sec}x=\frac{1}{\mathrm{cos}x}=-\frac{8}{5}=-1.60$

$\mathrm{csc}x=\frac{1}{\mathrm{sin}x}=\frac{1}{0.78}=1.28$

$\mathrm{tan}x=\frac{\mathrm{sin}x}{\mathrm{cos}x}=\frac{0.78}{-0.625}=-1.25$

$\mathrm{cot}x=\frac{1}{-1.25}=-0.80$

$\mathrm{sec}x=\frac{1}{\mathrm{cos}x}=-\frac{8}{5}=-1.60$

$\mathrm{csc}x=\frac{1}{\mathrm{sin}x}=\frac{1}{0.78}=1.28$