Question

Find trigonometric function of angles 180 and 270 degree

Answer 1

$\large\underline{\sf{Solution-}}$

$\red{\rm :\longmapsto\:sin(180\degree - x) = sinx}$

$\red{\rm :\longmapsto\:cos(180\degree - x) = - \: cosx}$

$\red{\rm :\longmapsto\:tan(180\degree - x) = - \: tanx}$

$\red{\rm :\longmapsto\:cosec(180\degree - x) = \: cosecx}$

$\red{\rm :\longmapsto\:sec(180\degree - x) = - \: secx}$

$\red{\rm :\longmapsto\:cot(180\degree - x) = - \: cotx}$

$\green{\rm :\longmapsto\:sin(180\degree + x) = - sinx}$

$\green{\rm :\longmapsto\:cos(180\degree + x) = - cosx}$

$\green{\rm :\longmapsto\:tan(180\degree + x) = tanx}$

$\green{\rm :\longmapsto\:cosec(180\degree + x) = - cosecx}$

$\green{\rm :\longmapsto\:sec(180\degree + x) = - secx}$

$\green{\rm :\longmapsto\:cot(180\degree + x) = cotx}$

$\blue{\rm :\longmapsto\:sin(270\degree - x) = - cosx}$

$\blue{\rm :\longmapsto\:cos(270\degree - x) = - sinx}$

$\blue{\rm :\longmapsto\:tan(270\degree - x) = cotx}$

$\blue{\rm :\longmapsto\:cosec(270\degree - x) = - secx}$

$\blue{\rm :\longmapsto\:sec(270\degree - x) = - cosecx}$

$\blue{\rm :\longmapsto\:cot(270\degree - x) = tanx}$

$\purple{\rm :\longmapsto\:sin(270\degree + x) = - cosx}$

$\purple{\rm :\longmapsto\:cos(270\degree + x) = sinx}$

$\purple{\rm :\longmapsto\:tan(270\degree + x) = - cotx}$

$\purple{\rm :\longmapsto\:cosec(270\degree + x) = - secx}$

$\purple{\rm :\longmapsto\:sec(270\degree + x) = cosecx}$

$\purple{\rm :\longmapsto\:cot(270\degree + x) = - tanx}$

Answer 2

Answer:

$\large\underline{\sf{Solution-}}$

$\red{\rm :\longmapsto\:sin(180\degree - x) = sinx}$

$\red{\rm :\longmapsto\:cos(180\degree - x) = - \: cosx}$

$\red{\rm :\longmapsto\:tan(180\degree - x) = - \: tanx}$

$\red{\rm :\longmapsto\:cosec(180\degree - x) = \: cosecx}$

$\red{\rm :\longmapsto\:sec(180\degree - x) = - \: secx}$

$\red{\rm :\longmapsto\:cot(180\degree - x) = - \: cotx}$

$\green{\rm :\longmapsto\:sin(180\degree + x) = - sinx}$

$\green{\rm :\longmapsto\:cos(180\degree + x) = - cosx}$

$\green{\rm :\longmapsto\:tan(180\degree + x) = tanx}$

$\green{\rm :\longmapsto\:cosec(180\degree + x) = - cosecx}$

$\green{\rm :\longmapsto\:sec(180\degree + x) = - secx}$

$\green{\rm :\longmapsto\:cot(180\degree + x) = cotx}$

$\blue{\rm :\longmapsto\:sin(270\degree - x) = - cosx}$

$\blue{\rm :\longmapsto\:cos(270\degree - x) = - sinx}$

$\blue{\rm :\longmapsto\:tan(270\degree - x) = cotx}$

$\blue{\rm :\longmapsto\:cosec(270\degree - x) = - secx}$

$\blue{\rm :\longmapsto\:sec(270\degree - x) = - cosecx}$

$\blue{\rm :\longmapsto\:cot(270\degree - x) = tanx}$

$\purple{\rm :\longmapsto\:sin(270\degree + x) = - cosx}$

$\purple{\rm :\longmapsto\:cos(270\degree + x) = sinx}$

$\purple{\rm :\longmapsto\:tan(270\degree + x) = - cotx}$

$\purple{\rm :\longmapsto\:cosec(270\degree + x) = - secx}$

$\purple{\rm :\longmapsto\:sec(270\degree + x) = cosecx}$

$\purple{\rm :\longmapsto\:cot(270\degree + x) = - tanx}$