How many exist such that ?

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- Oct 17th 2010, 01:46 PMHardworkInverse trigonometric equation
How many exist such that ?

- Oct 17th 2010, 01:49 PMAlso sprach Zarathustra
Just one.

- Oct 17th 2010, 01:50 PMHardwork
- Oct 17th 2010, 02:17 PMGeneral
There is a simple way:

Draw the graphs for the arcsin(x) & arccos(x),

The x-coordinate of the point of intersection is the solution. - Oct 17th 2010, 02:39 PMHardwork
- Oct 17th 2010, 03:22 PMskeeter
it's just a matter of being familiar with both functions.

has range

has range

the ranges intersect in quad I ... the angle in quad I that has the same sine and cosine value is

if you insist on doing it algebraically ...

... the negative solution is invalid since

and