anonymous
  • anonymous
Use identities (no calculators) to nd the exact value for (sin pi/4)(cos pi/2) + (cos pi/4)(sin pi/2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
this ones the hardest of them all
anonymous
  • anonymous
but if you have a look at it, see what expansion it looks like
anonymous
  • anonymous
and it becomes pretty easy

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anonymous
  • anonymous
this = sin(pi/4 + pi)??
anonymous
  • anonymous
no
anonymous
  • anonymous
sorry pi/2 + pi/4
anonymous
  • anonymous
=sin 3/4 pi = sin 75 degrees
anonymous
  • anonymous
i/m lost now!!
anonymous
  • anonymous
can sin 75 degrees be written in surd form?
anonymous
  • anonymous
its not 75 :|
anonymous
  • anonymous
but sin75 can be written in surd form
anonymous
  • anonymous
no hold om 3/4 pi = 3/4 X 180 = 135 degrees ruyght?
anonymous
  • anonymous
in which case sin 135 = 1 /sqrt 2
anonymous
  • anonymous
you can use sum angles expansion to find exact value of sin75 sin75 = sin(30+45) = sin30cos45+cos30sin45
anonymous
  • anonymous
yes
anonymous
  • anonymous
my brains not working to well today !
anonymous
  • anonymous
Mathematica returns zero after entering the problem expression. The left side of the + sign is zero because Sin[Pi]= zero. Same way for the right side.
watchmath
  • watchmath
It is equal to \(\sin(\frac{\pi}{4}+\frac{\pi}{2})=\sin(3\pi/4)=\sqrt{2}/2\)
anonymous
  • anonymous
(Sin pi/4) was processed as Sin(pi)/4 by Mathematica.
anonymous
  • anonymous
Wolfram may be incorrect but they are reporting that \[\text{Sin}\left[\frac{3 \pi }{4}\right]=\frac{1}{\sqrt{2}}\]

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