Answer to Question #192993 in Algebra for OhMoe

Question

If α is in quadrant 4, which quadrant is arccos(tanα) in? 

Answer 1

we know that how arccosine is restricted in quadrants,

The arccosine of a positive number is a first quadrant angle, cos^-1(+) is in quadrant I.

The arccosine of a negative number is a second quadrant angle,

cos^-1(-) is in quadrant II.

and we know that,

tan(x ) is negative in forth quadrant

so,

arccosine of -ve will be in second quadrant.

therefore,

arccos(tanα) will be in second quadrant.