can someone help me simplify these? this is soo frusrating, im about to cry.
cos(arctan(-1))
arccos(sin(-pie/2))
cot(arcsin 3/5)
sin (arccos (t))
thanks soo much!
Remember that $\displaystyle \sin^2(t)+\cos^2(t)=1 $.
Let $\displaystyle y=\arccos(t) \implies t=\cos(y) $.
Therefore $\displaystyle \sin^2(y)+\cos^2(y)=\sin^2(y)+t^2=1 $.
Thus $\displaystyle \sin^2(y)=1-t^2 \implies \sin(y)=\sqrt{1-t^2} $.
Now substitute $\displaystyle y=\arccos(t) $ back in to get $\displaystyle \sin(\arccos(t))=\sqrt{1-t^2} $.