Question 1153127
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The expression you show that is to be evaluated is almost certainly not right....<br>
In the expressions sin(x) or cos(x), x has to be the measurement of an angle; and the measurement is in radians unless degrees is specified.<br>
In the expression arcsin(x) or arccos(x), x has to be the value of the sine or cosine.<br>
So the expression sin(-4/7) which is part of the expression as you show it means the sine of an angle of -4/7 radians.  But it is highly probable that the -4/7 is supposed to be the sine of the angle (ratio of opposite side to hypotenuse, as in the calculation you did).<br>
In that case the correct expression to be evaluated is probably cos(arcsin(-4/7)).<br>
Note that arcsin(-4/7) is an angle in the 4th quadrant, where cosine is positive.<br>
Then, using your right triangle in the 4th quadrant, the opposite side is -4 and the hypotenuse is 7, making the adjacent side sqrt(33), as you calculated.<br>
Then the cosine of that angle is adjacent/hypotenuse = sqrt(33)/7.<br>