SLC 9 Review

3a

100

Convert 30° to radians.

π/6

200

Give positive/negative coterminal angles for 70°.

–430°, -290°

300

Convert −750 to radians.

-25π/6

400

Convert -5π/6 to degrees.

–150°

500

Arc length, r=10, angle=9π/8.

–A: s = 10·9π/8 = 45π/4

2d: Modeling Functions

100

Growth or decay? 80e^-0.14t

^Explain

Decay

200

A population grows from 30 to 80 in one month.

k = ln(80/30)

300

A drug decays 25% per hour from 125 mg.
Find the half-life.

When could the drug equal zero? 

2.41 hours

ln(0)

400

A bone has 20% of its original C-14.

Half-life = 5730 years.

How old is the bone? 

t≈13304.3

0.20=(12)t/5730

To solve for the exponent, we can take the natural logarithm of both sides:

ln(0.20)=ln[(12)t/5730]

Using the power rule for logarithms, we get:

ln(0.20)=t/5730ln(0.5)

t=ln(0.20)ln(0.5)×5730

t=-1.6094-0.6931×5730

t≈2.3219×5730

t≈13304.3

500

When does 80e^0.13t reach 200?

t≈6.6 years

3e1

100

What is the period of y=sin⁡x?

2π

200

What is the amplitude of 4cos⁡(x/3)−2?

4

300

What is the phase shift of y=−3sin⁡(2x−5)+7?

right 5/2

400

Evaluate sin⁡(4π+π/6).

1/2

500

Write a sinusoidal function with:

• amplitude 4

• period 2π/3

• midline y=−1

• phase shift π/4

y = 4sin(3x - π/4) - 1

3e2

100

What is the period of y=tan⁡x?

Pi

200

What is the period of y=cot⁡x?

Pi

300

Find all vertical asymptotes of f(x)=cot⁡(x+π/2) between −2π and 2π.

x = -π/2 + kπ

400

State the domain of f(x)=−3cot⁡(2x).

x ≠ kπ/2

500

Find the period of f(x)=2tan⁡(4x−32).

π/4

MISC.

100

In A₀e^kt, what does A₀ represent?

2d: Conceptual Question 

Initial value

200

Sketch one period of y=tan⁡(3x).
What is the period?

π/3

300

A graph has amplitude 3, midline 2, period 2π, and starts at its maximum at x=0 .
Write the equation.

 y = 3cos(x) + 2

400

Mercury travels a central angle of 4.1^∘ at radius 36 million miles.
Find the distance.

2.58 million miles

500

Identify the trig function with:

• period π

• asymptotes every π/2

• goes through (0,0)

y = tan x