helpplease1
Find exact value: sin(2 cos^-1(-3/11))
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zzr0ck3r
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there are infinite
helpplease1
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how so?
zzr0ck3r
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cos(x) = -3/11 has infinite solutions
zzr0ck3r
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forget what I said, they just want the one
zzr0ck3r
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cos^(-1)(-3/11) = 105.8
now
sin(105.8) = .9622
zzr0ck3r
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4sqrt(7)/11
helpplease1
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thank you!
surjithayer
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\[put \cos^{-1} \left( \frac{ -3 }{ 11 } \right)=x\]
\[\cos x=\frac{ -3 }{ 11 }\]
hence x lies in second or third quadrant.
\[\sin x=\sqrt{1-\left( \frac{ -3 }{11 } \right)^{2}}=\sqrt{1-\frac{ 9 }{121 }}=\frac{ \sqrt{112} }{11 }\]
sin x can be positive or negative according as x lies in second or third quadrant.
plug in sin 2x= 2 sin x cos x
helpplease1
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wow thank you so much!
surjithayer
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yw
zzr0ck3r
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woops I didn't notice the 2