Question

Tan x=4/3 x, lies in the 3rd quadrant find the value of other 5 trigonometric function

Answer 1

sec x = - 5/3,cos x= -3/5,sin x= - 4/5,cosec x= -5/3,cot x= -3/4

Step-by-step explanation:

√(1+ tan square x)= sec square x,

1/sec x = cos x

tan x = sin x /cos x,so sin x = tan x.cos x

and cot x = 1/tan x

signs are as for third quadrant only tans are positive, remaining all negative

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore sin\:x=\frac{-4}{5}}}$

${\bold{\therefore cos\:x=\frac{-3}{5}}}$

${\bold{\therefore cosec\:x=\frac{-5}{4}}}$

${\bold{\therefore sec\:x=\frac{-5}{3}}}$

${\bold{\therefore cot\:x=\frac{3}{4}}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{Given : } \\ \implies tan \: x = \frac{4}{3} \\ \\ \underline \bold{To \: Find : } \\ \implies sin \: x = ? \\ \\ \implies cos \: x = ? \\ \\ \implies cosec \: x = ? \\ \\ \implies sec\: x = ? \\ \\ \implies cot \: x = ?$

• According to given qustion :

$\bold{tan \: x \: lies \: on \: 3 rd \: quadrant} \\ \bold{So, \: value \: of \: p \: and \: b\: are \: in \: negative} \\ \\ \implies tan \: x = \frac{4}{3} \\ \\ \implies tan \: x = \frac{ - 4}{ - 3} \\ \\ \bold{by \: phythagoras \: theoram : } \\ \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ \implies {h}^{2} = ({ - 4})^{2} + ({ - 3})^{2} \\ \\ \implies {h}^{2} = 16 + 9 \\ \\ \implies {h} = \sqrt{25} \\ \\ \bold{\implies h = 5 \: cm} \\ \\ \bold{For \: trignometric \: function : } \\ \bold{sin \: x = \frac{p}{h} = \frac{ - 4}{5} } \\ \\ \bold{cos\: x = \frac{b}{h} = \frac{ - 3}{5} } \\ \\ \bold{cosec \: x = \frac{h}{b} = \frac{ - 5}{4} } \\ \\ \bold{sec \: x = \frac{h}{b} = \frac{ - 5}{3} } \\ \\ \bold{cot\: x = \frac{h}{p} = \frac{ 3}{4} }$