| 28 January |
Section 3.1.2: 7 (medium)
Section 3.1.1: 3 (easy, harder when you try only onto functions), 5 (easy when you start with simple cases), 6 (easy, seemingly hard) |
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| 26 January |
Write (1+i)^10 in the form a + ib with a and b real numbers.
(There is a clever easy method.)
Write (cos(π/6) + i sin(π/6))^9 in the form a + ib with a and b real numbers. (Think, this should not be hard.) Section 2.2.2: 2 (easy), 6de (seemingly hard) Section 2.2.1: 2 (easy), 6de (seemingly hard) Section 2.1.4: 2 (slightly technical), 8 (look for simple solutions) |
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| 21 January |
Use a geometric proof as in class to compute cos(π/10).
Then compute cos(π/5) and sin(π/5).
Find the repeated decimal representations of 1/27 and of 1/37. Then compute the product 27 * 37. Section 2.1.3: 2a (medium), 5 (medium) |
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| 14 January |
We had this nice mnemonic to remember the correct values of sin(0),
sin(π/6), sin(π/4), sin(π/3), and sin(π/2).
Write a similar table for cos(0), cos(π/6), cos(π/4), and so on.
Write a similar table for tan(0), tan(π/6), tan(π/4), and so on.
Section 2.1.2: 1 (straightforward) |
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| 12 January |
So we have the natural numbers N for ordinary counting, adding, and
even multiplication.
What makes the integers Z so special?
What makes the rationals Q so special?
What makes the reals R so special?
What makes the complex numbers C so special?
Section 2.1.1: 1 (easy), 2a (harder, try sqrt(7) - sqrt(8 - 2 sqrt(7)) first), 8 (think clearly). |