anonymous
  • anonymous
evaluate the exact value of : sin Pi/4-cos Pi/3+tan 3Pi/4-csc 5Pi/4+sec 4Pi/3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
assuming no calculator and only knowing unit circle?
anonymous
  • anonymous
yes because i need exact value and calculators only give me decimals
anonymous
  • anonymous
\[\tan \frac{ 3\pi }{ 4 }=\tan \left( \pi-\frac{ \pi }{4 } \right)=-\tan \frac{ \pi }{4 }=-1\]

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anonymous
  • anonymous
how did you get that?
anonymous
  • anonymous
Using unit circle you know exact values for sine/ cosine/ tangent, which is sine/cosine, csc, which is 1/sine, and sec which is 1/cosine
anonymous
  • anonymous
Shoot! i think i messed up signs let me check
anonymous
  • anonymous
oh my gosh I wrote it down wrong! I'm so sorry hold on! that first sin Pie/2 should be sin pie/4
anonymous
  • anonymous
ok well use The Unit Circle and substitute the correct values Sine corresponds to the Y values and Cosine corresponds to the X values of the unit circle http://en.wikipedia.org/wiki/File:Unit_circle_angles_color.svg
anonymous
  • anonymous
ok thank you
anonymous
  • anonymous
\[\csc \frac{ 5\pi }{4 }=\csc \left( \pi+\frac{ \pi }{4 } \right)=-\csc \frac{ \pi }{4 }=-\frac{ 1 }{ \ \sin \frac{ \pi }{ 4 } }=-\frac{ 1 }{ \frac{ 1 }{\sqrt{2} } }=-\sqrt{2}\] \[\sec \frac{ 4\pi }{ 3 }=\sec \left( \pi+\frac{ \pi }{3 } \right)=-\sec \frac{ \pi }{3 }=\frac{ -1 }{ \cos \frac{ \pi }{3 } }=\frac{ -1 }{ \frac{ 1 }{ 2 } } =-2\] \[\sin \frac{ \pi }{2 }=1\] \[\cos \frac{ \pi }{ 3 }=\frac{ 1 }{2 }\] now you can substitute the values and get the solution.
anonymous
  • anonymous
is this with the correct problem?
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok that you so much!
anonymous
  • anonymous
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anonymous
  • anonymous
\[\sqrt{\frac{ 1 }{4 }}=\frac{ 1 }{ 2 }\] similarly other values.

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