Math 160

Homework

Spring 2012

Dr. Wilson

1. 1/17 p66: 3, 7, 9, 13, 23, 25; p 72: 1, 3, 19, 31.

2. 1/19 p15: 3, 5, 11; pp24-25: 3, 5, 7, 11, 13; pp32-33: 1, 11, 15, 17, 23, 37.

3. 1/24 p112: 11, 13, 15.

4. 1/26 pp121-122: 35, 37, 39; pp134-135: 19, 23.

5. 2/2 pp157-158: 1, 3, 5, 7,9, 11, 13, 23, 25; pp164-165: 1, 2, 9, 11, 13, 15, 31.

6. 2/7 p92: 15, 17, 19. For each equation, find: the y-intercept, the x-intercept(s), and the vertex. Rewrite each equation to the form

y = a(x - h)2 + k.

7. 2/9 p400: 3, 7, 13; p406: 1, 3, 7, 11.

8. 2/16 p406: 5, 9; p413: 5, 7, 9, 11.

9. 2/21 p359: 7, 9, 11; p370: 3, 5, 7, 9, 15, 17, 21.

10. 2/23 pp304-305: 3, 7, 11, 23, 25, 27.

11. 2/28 Draw a unit circle in the Cartesian coordinate plane. Starting with 0o at (1, 0), and proceeding counterclockwise, mark off all the points on the circle whose angles are multiples of 30o and 45o. Label these points with their numbers of degrees, their numbers of radians, and their coordinates.

12. 3/1 Draw the graph of sin x and cos x with x measured in radians for x between 0 and 4 pi.

13. 3/6 pp275-276: 1, 3, 5, 9, 19. Make up a table with a row for each angle between 0 and 360 which is a multiple of 30o to 45o, and a columm for the number of degrees, the number of radians, the sine, cosine, tangent, cotangent, secant, and cosecant. draw the graphs of all of these functions measuring the angles in radians.

14. 3/8 pp292-293: 1, 3, 7, 9, 11, 13, 49, 51; pp311-312: 1, 3, 9, 11, 17.

15. 3/13 PP325-326: 1, 5, 7, 9, 11, 17, 21, 23.

16. 3/15 pp318-319: 5, 7, 15, 31, 33, 35.

17. 3/20 p340: 15, 17, 19, 21; p347: 5, 7, 17, 19, 23.

18 3/22 1. Write out Pascal's Triangle to the 16th row. In 2 - 5, compute: 2. (a + b)7. 3. (a - 3b)8. 4. 14C4. 5. 52C5. (Extra Credit) Express the height of the piston as a function of r, c, and theta.

19. 4/3 p504: 7, 11; p509: 7, 9, 11; Compute the square root of 5 to four places after the decimal point using the binmial theorem. (Hint: Use (4 + 1)1/2).

20: Compute e1/2 using the infinite series. Show the sequence of partial sums.

21. Compute the sine of pi/6 and the cosine of pi/3 using the infinite series for sine and cosine. Show the sequence of partial sums.

22. Compute ln3 using infinite sums. (Hint: ln3 = -ln(1/3) )

23. Derive the formula for the arc length of the arc of the unit circle from (0, 1) to (x, y) as a function of x.

24. Use the infinite series you get by integrating the power series you get by using the binomial theorem above to compute pi using the fact that pi/6 = arc sin (1/2)