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AP Calculus AB: 5.1.2 Graphing Trigonometric Functions

Mathematics10 CardsCreated 3 months ago

This flashcard set reviews key concepts for graphing trigonometric functions, including the importance of radian measure in calculus, conversion between degrees and radians, and recognizing features like amplitude and periodicity. It also includes simplification of common trig values and interpreting sine function graphs.

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Graphing Trigonometric Functions

  • Angles can be measured in degrees or radians. When using calculus, it is best to work with radian measure.

  • To convert from degrees to radians, multiply by π/180. To convert from radians to degrees, multiply by 180/π.

  • The graphs of the trigonometric functions are periodic. Use the sine and cosine curves to extrapolate the graphs of tangent, secant, cosecant, and cotangent.ngles can be measured in degrees or radians. When using calculus, it is best to work with radian measure.

  • To convert from degrees to radians, multiply by π/180. To convert from radians to degrees, multiply by 180/π.

  • The graphs of the trigonometric functions are periodic. Use the sine and cosine curves to extrapolate the graphs of tangent, secant, cosecant, and cotangent.

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Key Terms

Term
Definition

Graphing Trigonometric Functions

  • Angles can be measured in degrees or radians. When using calculus, it is best to work with radian measure.

  • To convert from d...

note

  • In geometry, most students use degree measure to describe angles.

  • However, degree measure is just one arbitrary way of
    de...

Convert 85° to radians.

85°=17π/36 radians

Convert 255° to radians.

17π/12 radians

Which of the following is the graph of y = 2 sin (x)?

graph with amplitude 2 and goes through origin

Simplify.

cosπ/4

√2/2

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AP Calculus AB: 5.1.2 Graphing Trigonometric Functions
TermDefinition

Graphing Trigonometric Functions

  • Angles can be measured in degrees or radians. When using calculus, it is best to work with radian measure.

  • To convert from degrees to radians, multiply by π/180. To convert from radians to degrees, multiply by 180/π.

  • The graphs of the trigonometric functions are periodic. Use the sine and cosine curves to extrapolate the graphs of tangent, secant, cosecant, and cotangent.ngles can be measured in degrees or radians. When using calculus, it is best to work with radian measure.

  • To convert from degrees to radians, multiply by π/180. To convert from radians to degrees, multiply by 180/π.

  • The graphs of the trigonometric functions are periodic. Use the sine and cosine curves to extrapolate the graphs of tangent, secant, cosecant, and cotangent.

note

  • In geometry, most students use degree measure to describe angles.

  • However, degree measure is just one arbitrary way of
    describing an angle.

  • In calculus, it is easier to use radian measure.

  • To convert between radians and degrees, it is important to remember that 360° is equal to 2π radians. From this relationship you can find any conversion you need.

  • There is a formula for converting between radians and
    degrees. To convert from degrees to radians, multiply by
    π/180. To convert from radians to degrees, multiply by 180/π.

  • Notice that the graphs of the sine and cosine functions are continuous. The graphs are also periodic—they repeat the same pattern over and over.

  • You can use the graphs of the sine function and the cosine function to graph other trig functions. Express the trig function you want to graph in terms of sine and cosine. Then evaluate that expression for different values of x.

  • Here is a table of important angles and the sine and cosine of those angles. You should either commit these values to memory or be able to derive them quickly.

  • Do not forget these essential identities.

Convert 85° to radians.

85°=17π/36 radians

Convert 255° to radians.

17π/12 radians

Which of the following is the graph of y = 2 sin (x)?

graph with amplitude 2 and goes through origin

Simplify.

cosπ/4

√2/2

Simplify.

sinπ/3

√3/2

When dealing with trigonometric functions in Calculus, it is important to use which method of angle measure?

Radian measure

Simplify.

cosπ/2

0

Convert 120° to radians

2π/3 radians