# Trig question, any help please?

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17 years ago
#1
Show that the inverse of cos x=the inverse of sin x has only one real root and state its exact value in surd form.

Any help would be much appreciated.
Cheers
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17 years ago
#2
Are u sure or am i wrong?well after sketching the two graphs we see that it actually has two real roots at x = 1/root2 and x = -1/root2

(this is because cos 45 = sin 45 and sin 225 = cos 225)
0
17 years ago
#3
answer in book gives root2/2 but doesnt show how to get it
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17 years ago
#4
Originally posted by Unregistered
Are u sure or am i wrong?well after sketching the two graphs we see that it actually has two real roots at x = 1/root2 and x = -1/root2

(this is because cos 45 = sin 45 and sin 225 = cos 225)
Drawing the graphs on a calculator shows that there's only one point where the graphs of arccos x and arcsin x intersect.
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17 years ago
#5
1/root two is the same as root two/two as its just rationalising the denominator
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17 years ago
#6
The domain's of the inverses of cos and sin are restricted to -1<=x<=1

If you draw the graphs seperately and then combine (arcsinx - arccosx = 0) you see that the root is about 1/root2 but how to prove algebraically I am unsure.
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