Question

If cos x is equals to 2 minus 3 by 5 , X lies in the third quadrant find the values of other five trigonometric functions explain

Answer 1

Answer:

$\bf{sinx=\frac{-4}{5}}$

$\bf{tanx=\frac{4}{3}}$

$\bf{cosecx=\frac{-5}{4}}$

$\bf{secx=\frac{-5}{3}}$

$\bf{cotx=\frac{3}{4}}$

Step-by-step explanation:

$\text{Given:}$

$cosx=\frac{-3}{5}$

$\text{we know that,}sin^2x=1-cos^2x$

$sin^2x=1-(\frac{-3}{5})2$

$sin^2x=1-\frac{9}{25}$

$sin^2x=\frac{25-9}{25}$

$sin^2x=\frac{16}{25}$

$sinx=\pm\frac{4}{5}$

But x lies in 3rd quadrant.

$\implies\:\bf{sinx=\frac{-4}{5}}$

Now,

$tanx=\frac{sinx}{cosx}$

$tanx=\frac{\frac{-4}{5}}{\frac{-3}{5}}$

$\implies\:\bf{tanx=\frac{4}{3}}$

$\bf{sinx=\frac{-4}{5}\implies\:cosecx=\frac{-5}{4}}$

$\bf{cosx=\frac{-3}{5}\implies\:secx=\frac{-5}{3}}$

$\bf{tanx=\frac{4}{3}\implies\:cotx=\frac{3}{4}}$