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Question

Find six trigonometric functions of 540°


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Solution

Find trigonometric ratios for the given expression:

Given, 540°

  1. sin540°+x=sin3π+x=-sinx [sinnπ+x=-sinx for nodd and 540°=3·180°=3π]
  2. cos540°+x=cos3π+x=-cosx[cosnπ+x=-cosx for nodd and 540°=3·180°=3π]
  3. tan540°+x=tan3π+x=tanx [tannπ+x=tanx for nodd and 540°=3·180°=3π]
  4. cot540°+x=1tan540°=1tan3π+x=1tanx=cotx[cotx=1tanx,,tannπ+x=tanx for nodd and 540°=3·180°=3π]
  5. sec540°+x=1cos540°+x=-1cosx=-sec(x)[sec(x)=1cosx,cosnπ+x=-cosx for nodd and 540°=3·180°=3π]
  6. cosec540°+x=1sin540°+x=-1sinx=-cosecx [cosecx=1sinx,sinnπ+x=-sinx for nodd and 540°=3·180°=3π]

Hence, six trigonometric functions of 540° is sin540°+x=-sinx,cos540°+x=-cosx,tan540°+x=tanx,cot(540°+x)=cotx,sec(540°+x)=-secxand cosec(540°+x)=-cosec(x).


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