Question:

Find sin(arccos(x))/cos(arcsin(x))

I am not sure if this helps to solve anything, and im not sure if this si correct or not.

=tan(arccos(x)/arcsin(x)

=tan(arccot(x))

=x

Thank you

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- Oct 13th 2012, 06:42 PMDylanRenkeFinding x in Trig
Question:

Find sin(arccos(x))/cos(arcsin(x))

I am not sure if this helps to solve anything, and im not sure if this si correct or not.

=tan(arccos(x)/arcsin(x)

=tan(arccot(x))

=x

Thank you - Oct 13th 2012, 06:56 PMMarkFLRe: Finding x in Trig
Hint: use the identity ...

- Oct 14th 2012, 11:51 AMSorobanRe: Finding x in Trig
Hello, DylanRenke!

Quote:

Let: .

The problem becomes: . .(a)

From [1]: /

We have: .

We have a right triangle with:

Pythagorus tells us that: .

Hence: . .(b)

From [2]: .

We have: .

We have a right triangle with:

Pythagorus tells us that: .

Hence: . .(c)

Substitute (b) and (c) into (a): .

- Oct 14th 2012, 12:29 PMHallsofIvyRe: Finding x in Trig
This is wrong. "arccos(x)/arcsin(x)" is NOT "arccot(x)". Just because a function has some property doesn't mean its inverse has that property!

Quote:

=x

Thank you

However, cosine and sine are not "one to one" functions so they do NOT, strictly speaking, have inverses. In order to be able to talk about "arccos(x)" and "arcsin(x)" we hage to restrict cosine to 0 to and sine to to [tex]\pi/2[/itex]. With those restrictions, sine and cosine are both postive and so both and are equal to [tex]\sqrt{1- x^2}[tex]. - Oct 14th 2012, 12:38 PMMarkFLRe: Finding x in Trig
If you use the hint I gave, you find:

- Oct 15th 2012, 04:54 PMDylanRenkeRe: Finding x in Trig
Thank you everybody.