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You need to know that the functions arcsine, arccosine and arctangent are inverses to trigonometric functions sine, cosine and tangent.
a) You need to remember that the domain of trigonometric functions comprises angles and the range comprises real values, hence the domain of inverse trigonometric functions comprises real values and not angles, hence there is not such a function as arccos `theta` (`theta` expresses an angle).
b) `arcsin (-sqrt 3)/4 = - arcsin (sqrt3)/4`
The function `- arcsin (sqrt3)/4` occurs if `sin(theta) = -sqrt3/4` and you need to find `theta` , thus `theta = arcsin (-sqrt 3)/4` .
c) `arctan (-sqrt3) = pi - arctan sqrt3`
The function `arctan (-sqrt3)` occurs if `tan(theta) = -sqrt3` and you need to find `theta` , thus `theta = arctan (-sqrt3) = pi - arctan sqrt3` .
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