How do you find the value of $sin(arccos1)$ ?

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Answer 1 · 2016-12-01T11:34:15

$sin(arccos(1)) = 0$

$y=arccos(x)$ is defined as the value of $y in [0,pi)$ for which $cos y =x$

In this interval $cosx =1$ for $x=0$ , so:

$arccos(1) = 0$

and then:

$sin(arccos(1)) = sin 0 = 0$

In general, for $x in [-1,1]$ as $arccosx$ is the inverse function of $cos x$ :

$cos(arccos x) = x$

and as for every $theta$

$sin theta = sqrt (1-cos^2 theta)$

$sin(arccos x) = sqrt (1-x^2 )$

which obviously brings to the same result.

How do you find the value of sin(arccos1)sin(arccos1)?