Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Pre-Calculus > Chapter 7 Trigonometry and Periodic Functions > Flashcards

Chapter 7 Trigonometry and Periodic Functions Flashcards

1
Q

Is the average rate of change in a periodic function constant?

A

No. It varies according to current period

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Periodic Functions

A

Functions with repeating values with regular intervals or periods

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Period

A

The distance between consecutive peaks in the graph of a periodic function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Midline

A

The horizontal line midway between the max and min values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Amplitude

A

The vertical distance from midline to peak

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Where on the unit circle would a zero degree angle be on?

A

The 3 O’clock position

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

From the zero angle, are degrees increments going counter clockwise or clockwise on the unit circle?

A

Counter-clockwise

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Can positive and negative angles be larger than 360 degrees?

A

Yes and if so they would continue to wrap around the circle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is the unit circle?

A

The circle of radius one centered at the origin point on a Cartesian graph.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

How are the points of the unit circle defined?

A

Using the sin and cosin functions

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What does the “sin” function output?

A

Given an angle that determines a point on the unit circle, the “sin” function determines the y-coordinate of the point on the unit circle.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What does the “cosin” function output?

A

Given an angle that determines a point on the unit circle, the “cosin” function determines the x-coordinate of the point on the unit circle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is a Reference Angle?

A

It is the angle measured to the nearest part of the x-axis and is always between 0 and 90 degrees and is opposite of the current angle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is a Radian?

A

a unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius

1rad × 180/π = 57.296°

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is the circumference of a circle?

A

C = 2(pi)r

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Using the circumference formula, how would you calculate the value of 1 radian?

A

1 radian = 360 degrees/(2(pi))

Which is equal to 57.296 degrees

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

How would you find the radians with a given angle?

A

2(pi)/(given degree)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is an arc length?

A

The arc length, s, spanned in a circle of radius r by an angle of (degree) in radians is

s = r(degree)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What is the domain and range of sine and cosin?

A

The domain is all real numbers

The range is between -1 and 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Is Sine an odd or even function? Explain what that means

A

It is an odd function which means the graph is symmetrical about the origin

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Is Cosine an even or odd function?

A

It is an even function which means that it is symmetrical about the y-axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What is the midline, amplitude and period of the sine and cosin functions?

A

The midline is found on y=0

The amplitude is 1

The period is 2(pi) which is equivalent to a full 360 degrees

23
Q

What is a sinusoidal function?

A

It is a periodic function graph showing regular oscillations

24
Q

What makes a function periodic?

A

A function is periodic if it’s values repeat at regular intervals

25
Q

What is the period of

sine(t) and sine(2t)

A

The period of sine(t) is 2(pi)

The period of sine(2t) is (pi)

26
Q

What is the formula to find out the period?

A

P=2(pi)/|B|

Where B is compression or stretching value like

y=sine(Bt) or y=cosine(Bt)

27
Q

What is the frequency?

A

The number of cycles in one unit of time

28
Q

Define the various variables in the following sinusoidal function

y = A(sine(Bt) + k

A

“A” is the amplitude

“B” is the compression/stretching value

“k” is the midline

“t” is the period

29
Q

What are the steps to finding a formula for an oscillating function?

A

Determine whether the graph is an odd or even function. That will determine whether it is a sine or cosine

Determine the k or midline value

Determine the A or amplitude value

Determine the Period between two max points

Use P=2(pi)/B to determine the B value

Plug all your values together

30
Q

How are sine and cosin related?

A

They are horizontal shifts of each other

31
Q

What is a phase shift?

A

It is a fraction of a period, more valuable in the real world, that the curve has shifted

32
Q

How do you get the phase shift?

A

From an unfactored horizontal shift value.

g(t) = cos(3t-(pi)/4)

Factored gives the horizontal shift value

g(t) = cos(3(t - (pi)/12))

33
Q

What does a positive and negative phase shift represent?

A

A positive phase shift value represents a shift to the left

A negative one represents a shift to the right

34
Q

What is a formula to calculate the phase shift?

A

(2(pi) * period)

35
Q

What does the tangent function represent?

A

The slope of the line through the origin and point (x,y)

36
Q

What does the tangent function equal?

A

tan() = sine/cosin

37
Q

What is the period of tan()?

A

It is pi

38
Q

Does tan() have an amplitude?

A

No because there is no max, min, or midline values

39
Q

At what points is tan() undefined and why?

A

Because the tan() = sine()/cosin()

Whenever cosin() = 0, tan() is undefined.

40
Q

What is the Pythagorean identity?

A

x^2 + y^2 = 1

Cosin^2 + Sine^2() = 1

41
Q

What is the secant() Function?

A

The inverse of cosin()

secant() = 1/cosin()

42
Q

What is cosecant()?

A

The inverse of sine()

csc() = 1/sine()

43
Q

What is the cotangent()?

A

The inverse of tan()

cot() = 1/tan()

44
Q

In terms of pi, what is the relationship of sine and cos?

A

sine t = cosin(t-(pi/2)) = -sine(-t)

cosin t = sine(t+(pi/2)) = cos(-t)

45
Q

What is the inverse cosine function?

A

Cos ^-1

Finds one of many possible angles whose cosine is a given value

Degree of angle = cos^-1(-0.4) = 1.982

46
Q

What is another way to refer to the inverse of cosine?

A

arccos()

47
Q

What is the domain of arccos?

A

Between 0 and pi

48
Q

What is the inverse sine function?

A

Determine the angle with the given sine value

sin^-1

49
Q

What is another way to refer to sine^-1?

A

Arcsine()

50
Q

What is the domain of arcsine()?

A

Between -(pi)/2 and pi/2

51
Q

What is the inverse tangent function?

A

tan^-1()

Gives the degree value for a given tangent value.

52
Q

What is another way to refer to the tan^-1?

A

Arctan()

53
Q

What is the domain and range of arctan()?

A

The domain is all real numbers

The range is between -(pi)/2 and pi/2

Pre-Calculus (8 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions