lilsis76
is x=15 degrees a solution of (( sqrt3)/3) cos2x+sin2x=1? how can i figure this out?
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campbell_st
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just substitute x = 15 into each trig ratio and use the exact angle identities below
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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
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how did you figure the triangle? even i didnt get or understand how to do that
lilsis76
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is the cos sqrt 3 / 2 and the sin 1/2?
campbell_st
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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
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okay let me try it. hold on
lilsis76
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|dw:1352143377873:dw|
lilsis76
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is this right? so it doesnt equal 1
campbell_st
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not quite |dw:1352143232742:dw|
lilsis76
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so it doesnt equal 1 still. right?
campbell_st
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yes it does you need to check the 1st part
|dw:1352143563524:dw|
lilsis76
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hold on let me try again, i wrote all sloppy
lilsis76
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|dw:1352144119351:dw|
campbell_st
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your question says
|dw:1352143923416:dw|
lilsis76
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yes
campbell_st
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substituting the exact values gives
|dw:1352143978828:dw|
lilsis76
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okay i see the 2x, is basically that value of cos that is the sqrt 3 /2
campbell_st
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thats right it x = 15 2x = 30 so you are using cos(30) and sin(30) which are known as exact values.
lilsis76
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|dw:1352144487645:dw|
campbell_st
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no |dw:1352144327997:dw|
lilsis76
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okay so the answer is 1/2, so the equation does not equal 1
campbell_st
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I'll write it again
|dw:1352144410590:dw|
lilsis76
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okay, so i would cross multiply to the the 6/6 to equal 1?