cos^-1(cos4pi/5) can someone help me with this one? And explain how they got the answer as well
Will fan and medal

Question

tkhunny · Answer

Cosine and Inverse Cosine are inverses.  Each un-does what the other did in the first place.

The obvious answer should be 4pi/5, but there could be more to it.  What do you think?

tkhunny · Answer

Rephrase:  IF you see that they are inverses, the result should be obvious.

It's a big if.  Do you see it?

anonymous · Answer

sin^-1(sin(-pi/10) @tkhunny Would the answer be -pi/10 then?

anonymous · Answer

may i help

anonymous · Answer

sure

tkhunny · Answer

Maybe. The technical problem is the Inverse Sine and Cosine Functions is their range.  Whatever the structure, it has to give you something in this range. You might thing it's just -pi/10, but that is it?  In this case, $\sin^{−1}(\sin(−π/10))=-π/10$, an angle in the right range but having the same sine.  Interestingly, $\cos^{−1}(\cos(−π/10))=+π/10$