A cosine function whose amplitude is 3 and period 2 π assuming a 0 . The equation of cosine curve is written as y = 3 cos θ where a 0 . Given: The amplitude a of cosine curve is 3 and period 2 π . Concept used: The cosine curve is of the form y = a cos b θ where a ≠ 0 and b 0 has an amplitude of a = a , period T = 2 π b and number of cycles b in the interval from 0 to 2 π . And if a 0 , use the five-point pattern of θ values which follows a pattern for y -values as max , 0 , min , 0 and max . Calculation: In order to sketch the graph of cosine function, evaluate the missing parameters using the concept stated above. As a = 3 and period T = 2 π . Therefore, the maximum and minimum value of the function is 3 and − 3 respectively. T = 2 π gives, 2 π b = 2 π b = 1 Since, the number of cycles b = 1 and amplitude a = 3 . Therefore, the equation of cosine curve of the form y = a cos b θ is written as y = 3 cos θ . Conclusion: The equation of cosine curve is written as y = 3 cos θ where a 0 .

Question

A cosine function whose amplitude is 3 and period 2 π assuming a > 0 . The equation of cosine curve is written as y = 3 cos θ where a > 0 . Given: The amplitude a of cosine curve is 3 and period 2 π . Concept used: The cosine curve is of the form y = a cos b θ where a ≠ 0 and b > 0 has an amplitude of a = a , period T = 2 π b and number of cycles b in the interval from 0 to 2 π . And if a > 0 , use the five-point pattern of θ values which follows a pattern for y -values as max , 0 , min , 0 and max . Calculation: In order to sketch the graph of cosine function, evaluate the missing parameters using the concept stated above. As a = 3 and period T = 2 π . Therefore, the maximum and minimum value of the function is 3 and − 3 respectively. T = 2 π gives, 2 π b = 2 π b = 1 Since, the number of cycles b = 1 and amplitude a = 3 . Therefore, the equation of cosine curve of the form y = a cos b θ is written as y = 3 cos θ . Conclusion: The equation of cosine curve is written as y = 3 cos θ where a > 0 .

Filo · Accepted Answer

-->To write: A cosine function whose amplitude is 3 and period 2π assuming a>0 .-->-->The equation of cosine curve is written as y=3cosθ where a>0 .-->-->Given:The amplitude a of cosine curve is 3 and period 2π .Concept used:The cosine curve is of the form y=acosbθ where a≠0 and b>0 has an amplitude of a=a , period T=2πb and number of cycles b in the interval from 0 to 2π . And if a>0 , use the five-point pattern of θ values which follows a pattern for y -values as max, 0, min, 0 and max .Calculation:In order to sketch the graph of cosine function, evaluate the missing parameters using the concept stated above.As a=3 and period T=2π . Therefore, the maximum and minimum value of the function is 3 and −3 respectively.  T=2π gives,2πb=2πb=1Since, the number of cycles b=1 and amplitude a=3 . Therefore, the equation of cosine curve of the form y=acosbθ is written as y=3cosθ .Conclusion:The equation of cosine curve is written as y=3cosθ where a>0 .-->

Question Text	A cosine function whose amplitude is 3 and period 2 π assuming a > 0 . The equation of cosine curve is written as y = 3 cos θ where a > 0 . Given: The amplitude a of cosine curve is 3 and period 2 π . Concept used: The cosine curve is of the form y = a cos b θ where a ≠ 0 and b > 0 has an amplitude of a = a , period T = 2 π b and number of cycles b in the interval from 0 to 2 π . And if a > 0 , use the five-point pattern of θ values which follows a pattern for y -values as max , 0 , min , 0 and max . Calculation: In order to sketch the graph of cosine function, evaluate the missing parameters using the concept stated above. As a = 3 and period T = 2 π . Therefore, the maximum and minimum value of the function is 3 and − 3 respectively. T = 2 π gives, 2 π b = 2 π b = 1 Since, the number of cycles b = 1 and amplitude a = 3 . Therefore, the equation of cosine curve of the form y = a cos b θ is written as y = 3 cos θ . Conclusion: The equation of cosine curve is written as y = 3 cos θ where a > 0 .
Topic	All Topics
Subject	Algebra 2
Class	Class 11
Answer Type	Text solution:1

Text solutionVerified

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