Marx Versus Keynes: The Economic Debate

Marx Versus Keynes: The Economic Debate
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In this discussion between Marx and Keynes, the contrasting views on value, production, crises, and the future of the economy are examined. While Marx emphasizes labor theory of value and production for profit, Keynes focuses on marginalism and the temporary lack of demand. The debate explores fundamental economic concepts and their implications for modern society.

  • Marx
  • Keynes
  • Economics
  • Value Theory
  • Production

Uploaded on Mar 01, 2025 | 0 Views


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  1. Bellwork Find one positive angle and one negative angle in standard position that are coterminal with the given angle. 1. 135 2. 11 6

  2. Extra Practice Find one positive and one negative angle that is coterminal with the angle = in standard position. Find one positive and one negative angle that is coterminal with the angle = in standard position. 3 7 5

  3. Trigonometric Functions of Any Angle Section 9.3

  4. What You Will Learn Evaluate trigonometric functions of any angle. Find and use reference angles to evaluate trigonometric functions

  5. Take Note

  6. Example: Evaluating Trigonometric Functions Given a Point Let ( 4, 3) be a point on the terminal side of an angle in standard position. Evaluate the six trigonometric functions of .

  7. Take Note It is convenient to use the unit circle to find trigonometric functions of quadrantal angles. A quadrantal angle is an angle in standard position whose terminal side lies on an axis. The measure of a quadrantal angle is always a multiple of 90 , or /2 radians.

  8. Using the Unit Circle Use the unit circle to evaluate the six trigonometric functions of = 270 . Find the values of the six trigonometric functions. Let x = 0 and y = 1 to evaluate the trigonometric functions.

  9. Take Note

  10. Reference angle Let be an angle in standard position. Its reference angle is the acute angle formed by the terminal side of and the horizontal axis. 11

  11. Take Note

  12. Reference angles are always measured between the x axis and the terminal side of the angle (always +ves !) Notice the butterfly shape 13

  13. Finding the Trig functions of any angle tan135 = Find the reference angle = 1. 180 45 135 ref = Determine the value of the given trig function of the reference angle. 2. = tan45 1 Determine the sign based on the quadrant of the given (original) angle 3. Q 135 II tan II is in Q = tan135 1 14

  14. Drawing Reference Angles Find the reference angle ' , and sketch and ' in standard position. 1) = -145 11 = 2) 3 15

  15. Using Reference Angles to Evaluate Functions Evaluate (a) tan( 240 ) and (b) csc 17 /6 .

  16. Now: Find all 6 trig functions of an angle Find the six trigonometric functions of with the given constraint. 15 8 = tan ; sin 0 17

  17. Now, lets make it tougher The terminal side of lies on the line y = (1/3)x in quadrant I. Find the values of the 6 trig functions of by finding a point on the line. sin = cos = csc = sec = tan = cot = 18

  18. Bellwork The terminal side of lies on the line y = (3/4)x in quadrant III. Find the values of the 6 trig functions of by finding a point on the line. sin = cos = csc = sec = tan = cot = 19

  19. Try These: Find the values of the six trig functions of with the given constraints. sin = 0; where sec = -1 Find the reference angle and sketch it and the angle in standard position. a) = 3.5 b) = 750 20

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