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Answers To The Exercises: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14
Lesson 13
 


13.1.
b) and c).

13.2.
On this interval, the sine function is not monotonic (see details in the answer to the problem 12.1).

13.3.
Any range can be used, on which the sine satisfies two conditions:
1) it is monotonic; 2) it takes all values from –1 to 1.
One of the examples is the interval [/2, 3/2].

13.4.
1) 20°;  2) 100°;  3) 20°;  4) 80° (80° = 180° – 100°);  5) –80°.

13.5.
1) /4;  2) /3;  3) /2;  4) 0;  5)/2;  6) /6.

13.6.
x = (–1)n ·0.85 + n.

13.7.

13.8.
b) and c).

13.9.
The domain is the interval (– , ). The range is the interval (–/2, /2).

13.10.
1) /6;  2)/6;  3) /4;  4) 0;  5) /4.

13.11
x = 0.46 + n.

13.12
Take the graph of arctan x, and shift it one unit to the right and one unit up.

13.13.
a), b) and d). As main segments, the intervals (0, ) and (, 2) may be used. The best candidate is the interval (0, ).

13.14.
The arccot x is the angle from the interval (0, ) whose cotangent is equal to x.

13.15.

13.16.
x = arccot A + n.

 

 

 

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