Unit Circle
What is the value of Cos(π/6)
√3/2
Concave up means that the rate of change is doing what?
Increasing
How many petals does r=4cos(2x) have?
4 petals.
What is the amplitude of the function y=2sin(1/2x)?
2
What is the value of arc sin (1)?
π/2
What is the angle of sin(π/4)?
45 degrees
What is a period?
The distance between repetitions on a periodic function.
What does r=4 look like on a graph?
It is a circle with a center of (0,0) and a radius of 4.
What is the period of the graph y=3cos(2x)
π
What is the value of arc cos (-1/2)
2π/3
What is the value of tan(135°)?
-1
Which of the following scenarios represent a periodic function over time?
a) The height of a ball that is bounced off the ground has a maximum of 10 ft.
b)The total value of an account that increases by $100 dollars every week and earns 5% interest.
c)The lung volume that cycles between 3000 and 1200 mL of air as a person breaths.
C
The polar function 𝑟 = 𝑓(𝜃), where 𝑓(𝜃) = 𝜋
3 𝜃, is defined for 𝜃 > 0. Which of the following describes the graph of 𝑟 = 𝑓(𝜃) in the polar coordinate system?
(A) The graph of 𝑟 = 𝑓(𝜃) is line along the angle 𝜋/3.
(B) The graph of 𝑟 = 𝑓(𝜃) is a circle with radius of 𝜋/3.
(C) The graph of 𝑟 = 𝑓(𝜃) is a spiral with increasing radius
(D) The graph of 𝑟 = 𝑓(𝜃) is a spiral with decreasing radius
(C) The graph of 𝑟 = 𝑓(𝜃) is a spiral with increasing radius
The function of f is defined by f(x)=4tan(2x)+5. What is the period of f?
π/2
What is the value of arc tan (1)?
π/4
What is the value of csc(3π/4)?
-√2
A particular species of bird chirps in a cycle that lasts 8 seconds. The chirping starts off quiet, grows to its loudest at 120 dB after 4 seconds, and then gradually gets quieter again.
If we were to graph this on a decibel scale, what will be starting point?
The x-coordinate will be x=0 to serve as the starting point and since the chirping starts off quiet the y-coordinate will be y=0.
Or (0,0)
Consider the graph of the polar function r=fθ, where fθ=2sinθ-1, in the polar coordinate system. Which of the following descriptions is true?
A) As θ increases from 0 to π6, the polar function r=f(θ) is increasing, and the distance between the point (f(θ),θ) on the curve and the origin is increasing.
B) As θ increases from 0 to π6, the polar function r=f(θ) is increasing, and the distance between the point (f(θ),θ) on the curve and the origin is decreasing.
C) As θ increases from 0 to π/6, the polar function r=f(θ) is decreasing, and the distance between the point (f(θ),θ) on the curve and the origin is increasing.
What is the range of the function y=3sin(x)?
-3≤y≤3
What is the value of arc sin (cos 0)?
π/2
What is 5π in degrees?
900 degrees
F is a periodic function with a period of k. Which of the following values are always equivalent to f(3)?
1. f(k)
2. f(3+3k)
3. f(3k)
2
Which of the following expresses the complex number 10+10i using polar coordinates in the form (rcosθ)+i(rsinθ)?
(10√2cos(π/4))+i(10√2sin(π/4))
In Myrtle Beach, South Carolina, the height of the tide, in feet (ft), is modeled by the function H , defined by H(t)=2.1 sin(π/6(t-1))+2.6 for hours 0 to 12. Based on this model, which of the following is true?
A) The maximum height of the tide is 4.7 feet.
(B) The maximum height of the tide occurs at t=1 hours.
(C) The minimum height of the tide is 2.6 feet.
(D) The minimum height of the tide occurs at t=1 hours
A
What is the value of arc cos (sin 4π/3)?
5π/6