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### PreCalculus

'20-'21 PreCalc Students:
here's your supply list for class.

I'm looking forward to August! Enjoy the remainder of your summer.

• binder with loose leaf paper OR spiral notebook with pockets and enough paper to last all school year-for MATH only! (A 1-inch binder with a zippered pencil pouch works best.)
• pencils, pens (dark blue or black for regular classroom purposes),
• large eraser
• colored pencils or an assortment of colored pens for graphing
• graph paper
• protractor
• box of facial tissues and container of disinfecting wipes
Week Six Assignments (Friday, May 15-Thursday, May 21)

Web-Based
You’ll work on trigonometric concepts.

Non Web-Based
Suppose you invest \$1500 in an account with an interest rate of 8% for 12 years, making no other deposits or withdrawals.
a) What will be your account balance if the interest is compounded monthly?

b) What will be your account balance if the interest is compounded continuously?

c) If the investment is compounded daily, about how long will it take for it to be worth double the initial amount?

SOLUTIONS to Week Six
a) A=1500(1+(0.08/12))¹⁴⁴
A= \$3,905.08

b) A= 1800e⁽⁰˙⁰⁸*¹²⁾       (The exponent is 0.08 times 12.)
A=\$3917.54

c) 1500(1 + (.08/365))³⁶⁵ᵗ= 3000

(1 + (.08/365))³⁶⁵ᵗ = 2

365t * ln(1 + (.08/365))= ln2

t≈8.67 years

Week Five Assignments (Friday, May 8-Thursday, May 15)

Web-Based

You’ll work on trigonometric concepts.

Non Web-Based
Solve each equation. I apologize that my superscript enhancement isn't easy to read.

1. 3ⁿ⁺³ = 27ⁿ⁻²

2. eⁿ - 4e⁻ⁿ = 0

3.  log₆x + log₆(x-5) =2

Solutions to Week Five
1.  Change 27 to 3³. Once the bases are the same on each side of the equation, solve for the exponents.
n+3=3(n-2).     n=4.5

2.  Factor the expression on the left:
eⁿ(1-4e⁻²ˣ)=0      eⁿ= 0 has no solution
1-4e⁻²ˣ=0

4e⁻²ˣ=1    ⟹      e⁻²ˣ=1/4   ⟹ ln e⁻²ˣ = ln (1/4)   ⟹ -2x=ln (1/4) ⟹ x=ln (1/4)⁻⁰﹒⁵

x= ln2

3. log₆ x(x-5)=2  ⟹  6ˡºᵍ⁽ᵇªˢᵉ ⁶⁾ˣ⁽ˣ⁻⁵⁾=6² ⇒  x(x-5) = 36 ⇒ x²-5x-35=0

(x-9)(x+4)=0   ⇒x=-4 is undefined; x=9

Week Four Assignments (Friday, May 1-Thursday, May 7)

Web-Based

You’ll work on trigonometric concepts.

Non Web-Based
Graph each function. Use radians for the domain (along the x-axis).
1. f(x)= cos 𝜃
2. g(x) = 5 cos 𝜃 -2
3. h(x) = -cos (𝜃-(𝝿/3))

Solutions to Week 4
1. Graph the basic cosine function with the five key points for interval [0,𝛑] are:
(0,1), (𝛑/2, 0), (𝛑, -1), (3𝝿/2, 0), (2𝛑, 1).

2. This cosine graph has an altitude of 5 and is then displaced two (2) units down. The five key points are for interval [0,𝛑] are:
(0,3), (𝛑/2, -2), (𝛑, -7), (3𝝿/2, -2), (2𝛑, 3).

3. This cosine graph is inverted, then shifted horizontally by 𝝿/3 to the right. The five key points are for interval [0,𝛑] are: (𝝿/3, -1), (5𝛑/6,0), (4𝛑/3, 1), (11𝝿/6, 0), (7𝝿/3, -1)

Week Three Assignments (Friday, April 24-Thursday, April 30)

Web-Based

You’ll work on trigonometric concepts.

Non Web-Based
Convert each degree measure into radians as a multiple of 𝛑 and each radian measure in degrees.
1. 450 degrees

2. 5𝝿/6

3.
780 degrees
4. 15𝝿/12

Solutions to Week Three

1. 450˚(𝝿/180˚)=5𝝿/2
2. 5𝝿/6
(180˚/𝝿)=150˚
3.
780˚(𝝿/180˚)=13𝝿/3
4. 15𝝿/12(180˚/𝛑)=225˚

Week Two Assignments (Friday, April 17-Thursday, April 23)

Web-Based

You’ll work on trigonometric concepts.

Non Web-Based
Use the unit circle to find the exact values of
1.
sin (5𝛑/3)
2.
cos(7𝛑/6)
3.
tan(3𝛑/4)
Solutions to Week 2
1. sin (5𝛑/3)=-√3/2
2.
cos(7𝛑/6)=-√3/2
3.
tan(3𝛑/4)
= -1

Week One Assignments (Friday, April 10-Thursday, April 16)

Web-Based

You’ll work on trigonometric concepts.

Non Web-Based
1. Graph two (2) cycles of y=sin x.
Solution: The basic cycle for the sine function, using five (5) key points:
(0,0),  (𝝿/2, 1),
(𝝿, 0),  (3𝝿/2, -1), and (2𝝿, 0). Connect these points with a gentle sine wave.
2. Graph two cycles of y=3 sin x.
The x coordinates remain the same as in problem 1,  but each y-coordinate is multiplied by 3.
The five key points are (0,0),  (𝝿/2, 3),  (𝝿, 0),  (3𝝿/2, -3), and (2𝝿, 0).

3. Graph two cycles of y= 3 sin x-3.
Subtract three (3) from each y-coordinate from problem 2.
The five key points are (0,-3),  (𝝿/2, 0),  (𝝿, -3),  (3𝝿/2, -6), and (2𝝿, -3).