5.1.2 Graphing Trigonometric Functions

Question 1

Graphing Trigonometric Functions

Answer 1

• 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.

Question 2

note

Answer 2

• 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.

Question 3

Convert 85° to radians.

Answer 3

85°=17π/36 radians

Question 4

Convert 255° to radians.

Answer 4

17π/12 radians

Question 5

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

Answer 5

graph with amplitude 2 and goes through origin

Question 6

Simplify.

cosπ/4

Answer 6

√2/2

Question 7

Simplify.

sinπ/3

Answer 7

√3/2

Question 8

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

Answer 8

Radian measure

Question 9

Simplify.

cosπ/2

Answer 9

0

Question 10

Convert 120° to radians

Answer 10

2π/3 radians