Question

find the values of other half trigonometric functions : cotx=3/5,x lies in third quadrant​

Answer 1

Answer:

$\cot(x) = \frac{3}{4}$

so,

$\tan(x) = \frac{1}{ \cot(x) } = \frac{4}{3}$

Now ∵1+tan² x=sec² x

$= {sec}^{2} x = 1 + \frac{16}{9}$

${sec}^{2} x = \frac{25}{9}$

$sec \: x = \binom{ + }{ - } \frac{5}{3}$

Since x lies in third quadrant, the value of sec x will be negative.

$\csc(x) = \frac{1}{sin \: x } = - \frac{5}{4}$

$∴ \: sec \: x = - \frac{5}{3} </p><p></p><p>$

$\cos(x ) = \frac{1}{sec \: x} \: - \frac{3}{5}$

$\tan(x) = \frac{sin \: x}{ \cos \: x}$

$\sin(x) = ( \frac{4}{3} ) \times ( - \frac{3}{5} ) = - \frac{4}{5}$