lilsis76
  • lilsis76
is x=15 degrees a solution of (( sqrt3)/3) cos2x+sin2x=1? how can i figure this out?
Mathematics
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SOLVED
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chestercat
  • chestercat
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campbell_st
  • campbell_st
just substitute x = 15 into each trig ratio and use the exact angle identities below |dw:1352142650262:dw| if x =15 then 2x = 30.... use the exact values from the triangle above for cos2(15) = cos(30) ans sin2(15) = sin(30)
lilsis76
  • lilsis76
how did you figure the triangle? even i didnt get or understand how to do that
lilsis76
  • lilsis76
is the cos sqrt 3 / 2 and the sin 1/2?

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campbell_st
  • campbell_st
its called the an exact value triangle and its usually taught during a topic on trigonometry. thats correct now substitute those values to show that you will get 1 as the answer,
lilsis76
  • lilsis76
okay let me try it. hold on
lilsis76
  • lilsis76
|dw:1352143377873:dw|
lilsis76
  • lilsis76
is this right? so it doesnt equal 1
campbell_st
  • campbell_st
not quite |dw:1352143232742:dw|
lilsis76
  • lilsis76
so it doesnt equal 1 still. right?
campbell_st
  • campbell_st
yes it does you need to check the 1st part |dw:1352143563524:dw|
lilsis76
  • lilsis76
hold on let me try again, i wrote all sloppy
lilsis76
  • lilsis76
|dw:1352144119351:dw|
campbell_st
  • campbell_st
your question says |dw:1352143923416:dw|
lilsis76
  • lilsis76
yes
campbell_st
  • campbell_st
substituting the exact values gives |dw:1352143978828:dw|
lilsis76
  • lilsis76
okay i see the 2x, is basically that value of cos that is the sqrt 3 /2
campbell_st
  • campbell_st
thats right it x = 15 2x = 30 so you are using cos(30) and sin(30) which are known as exact values.
lilsis76
  • lilsis76
|dw:1352144487645:dw|
campbell_st
  • campbell_st
no |dw:1352144327997:dw|
lilsis76
  • lilsis76
okay so the answer is 1/2, so the equation does not equal 1
campbell_st
  • campbell_st
I'll write it again |dw:1352144410590:dw|
lilsis76
  • lilsis76
okay, so i would cross multiply to the the 6/6 to equal 1?

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