The discussion revolves around evaluating the expression cos(ArcSec(-√2 + π/4)) and understanding the relationship between the angle π/4 and its cosine value. Participants explore the implications of substituting π/4 with its approximate decimal value and the properties of the arcsecant function.
The discussion is active, with participants providing insights into the properties of trigonometric functions. Some guidance has been offered regarding the simplification of the expression, and there is a recognition of confusion surrounding the use of π/4. Multiple interpretations of the problem are being explored.
There is a mention of the principal range of arcsec and the potential confusion arising from the inclusion of π/4 in the expression. Participants are navigating through assumptions about the values involved in the trigonometric functions.
yyat said:Hi Nyasha!
Why do you think that [tex]\frac{\pi}{4}\approx .785[/tex] is the same as [tex]\frac{\sqrt{2}}{2}\approx .707[/tex]?
You can however simplify cos(arcsec(...)).
yyat said:Well, you don't need to use decimal notation (and probably should not in this case), I was just trying to demonstrate that the two numbers are not the same.
What I was hinting at before: sec(x)=1/cos(x), so arcsec(x)=arccos(1/x) and also cos(arccos(x))=x by definition. Use this to simplify your expression.
yyat said:Well, you don't need to use decimal notation (and probably should not in this case), I was just trying to demonstrate that the two numbers are not the same.
What I was hinting at before: sec(x)=1/cos(x), so arcsec(x)=arccos(1/x) and also cos(arccos(x))=x by definition. Use this to simplify your expression.
Yes it was : [tex]\{cos}(\text{arcsec}(-\sqrt{2})+\frac{\pi}{4})[/tex]yyat said:So it really was [tex]\text{cos}(\text{arcsec}(-\sqrt{2})+\frac{\pi}{4})[/tex]? Otherwise, it is not correct.