Determine an approximate measure of theta in radians

Question

Angle theta lies in the second quadrant and sinθ=7/25.

 

when i do arccos of -24/25 i get a different answer than when i do arcsin7/25 and only arccos of -24/25 is correct.

 

why is this?

Answer 1

The mistake you may be making is that when you take the arcos of -24/25 and use the calculator, it usually will give you a negative answer in which case it would be in the third quadrant to be consistent with taking the arccos of a negative number. My suggesting is to take the arcsin of 7/25 and than subtract it from pi to get the correct angle that is in the second quadrant.