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f(x)= 4\cos\theta+\sin^2\theta

Which of the follwing is true for f(x)?

Option: 1

At \theta=0 f(x) has its maximum value and maximum value of f(x) is 5


Option: 2

At \theta=\pi f(x) has its minimum and minimum value of f(x) is -5


Option: 3

At \theta=\pi f(x) has its minimum value and minimum value of f(x) is -4


Option: 4

At \theta=0 f(x) has its minimum value and minimum value of f(x) is 1


Answers (1)

best_answer

 

Graph of Trigonometric Function (Part 1) -

Graph of Trigonometric Function (Part 1)

 

Cosine Function

y = f(x)= cos(x)

 

Domain is R 

Range is [-1, 1]

 

-

 

f(x)= 4\cos\theta+\sin^2\theta\\ =4\cos\theta+1-\cos^2\theta\\ =5-(\cos^2-4\cos\theta+4)\\ =5-(\cos\theta-2)^2\\

 

minimum value of f(x) at \theta=\pi

f(x)min=5-9=-4

maximum value of f(x) at \theta=0

f(x)max=5-1=4

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shivangi.shekhar

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