Precalculus
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OpenStudy (anonymous):
Find the exact value of the expression.
cos(arcsin1/2+arccotroot 3/3)
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hartnn (hartnn):
arcsin 1/2= ?
can u evaluate that?
OpenStudy (anonymous):
means \[\sin^{-1} (1/2) \]
OpenStudy (anonymous):
im lost
hartnn (hartnn):
for what angle is the value of sin 1/2 = ?
OpenStudy (anonymous):
60 degrees
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hartnn (hartnn):
nopes, sin 60 = root 3/2
sin 30 = 1/2
hartnn (hartnn):
so arcsin 1/2 = 30 degrees, ok ?
OpenStudy (anonymous):
ok
hartnn (hartnn):
and for what angle is cot x = root 3/3 or 1/ root 3 ?
OpenStudy (anonymous):
30?
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hartnn (hartnn):
cot 30 - root 3, cot 60 = 1/root 3
hartnn (hartnn):
so u have arccotroot 3/3 = 60
so what is the value of arcsin1/2+arccotroot 3/3 = ?
hartnn (hartnn):
@Zekarias arcsin 1/2 = 60 ?
hartnn (hartnn):
arcsin1/2+arccotroot 3/3 = 30+60= ?
OpenStudy (anonymous):
u lost me
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hartnn (hartnn):
u clear with arcsin 1/2 = 30 ?
hartnn (hartnn):
because sin 30 = 1/2
OpenStudy (anonymous):
okay
hartnn (hartnn):
arccotroot 3/3 = 60
because
cot 60 =1/ (root 3) = root 3/3
hartnn (hartnn):
so arcsin1/2+arccotroot 3/3 = 30+60= ?
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OpenStudy (anonymous):
90 ?
hartnn (hartnn):
yeah, clear till here ?
OpenStudy (anonymous):
yup
hartnn (hartnn):
cos(arcsin1/2+arccotroot 3/3)
=cos 90 = ?
OpenStudy (anonymous):
0
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hartnn (hartnn):
that is correct and is the final answer :)
OpenStudy (anonymous):
ohh ok thank you
hartnn (hartnn):
welcome ^_^