sin(cos–1 0.6372)

Good point, Melody.

We would need to involve the quadrant diagram for a complete answer.

You could use a rule for this, but it is more instructive to work it out from first principles:

draw a right-angled triangle, choose one of the acute angles to be our angle x, so denote the length of its ADJACENT side as 0.6372, and the length of the HYPOTENUSE as 1.000 . This means we've made cos x = 0.6372

Use Pythagoras' Theorem to determine the length of the unknown side.

Inspect the triangle and write down the ratio of the two sides that determine sin x,

i.e., opposite/hypotenuse

Done!

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Thanks Badinage,

I usually do it that way too.   But be warned ..... :)

I entered   sin(acos( 0.6372))

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.637\: \!2}}\right)}\right)} = {\mathtt{0.770\: \!698\: \!488\: \!386}}$$

Only thing you need to be careful of is the sign.

Cos is pos in the 1st and 4th quad.   Sin is pos in the 1st but neg in the 4th 

so

the answer can be     + or -   0.7707