On this interval, the sine function is not monotonic (see details in the answer to the problem 12.1).
1) it is monotonic; 2) it takes all values from –1 to 1.
One of the examples is the interval [ /2, 3 /2].
1) 20°; 2) 100°; 3) 20°; 4) 80° (80° = 180° – 100°); 5) –80°.
1) /4; 2) – /3; 3) /2; 4) 0; 5) – /2; 6) /6.
x = (–1)n ·0.85 + n.
The domain is the interval (– , ). The range is the interval (– /2, /2).
1) /6; 2) – /6; 3) /4; 4) 0; 5) – /4.
x = 0.46 + n.
Take the graph of arctan x, and shift it one unit to the right and one unit up.
a), b) and d). As main segments, the intervals (0, ) and ( , 2 ) may be used. The best candidate is the interval (0, ).
The arccot x is the angle from the interval (0, ) whose cotangent is equal to x.
x = arccot A + n.