Arccos(cos230)+arcsin(sin(-400)+arctg(tg110)

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вопрос

To simplify this expression, we need to remember that arccos(x) and arcsin(x) are the inverse functions of cos(x) and sin(x) respectively, while arctg(x) is the inverse function of tg(x) (also known as tan(x)).

So, we have:

arccos(cos(230)) + arcsin(sin(-400)) + arctg(tg(110))

First let's simplify each part individually:

arccos(cos(230))
Since cos(230) is in the range between -1 and 1, the value is within the domain of arccos(x). So, arccos(cos(230)) simplifies to 230.

arcsin(sin(-400))
Since sin(-400) is in the range between -1 and 1, the value is within the domain of arcsin(x). sin(-400) = sin(360-40) = sin(40) because sin has a period of 360 degrees. So, this simplifies to arcsin(sin(40)) which means the answer is 40.

arctg(tg(110))
Since tg(110) = tg(110 - 180) = tg(-70). The arctg(x) function has a range between -π/2 and π/2, which doesn't include -70 degrees. Therefore, the expression arctg(tg(110)) is undefined.

Putting it all together, we have:

230 + 40 + undefine
= 270 + undefined

Therefore, the final simplified expression is 270 + undefined.