Given the function f (x) = 3sinx + 4cosx, the maximum value of F (x) is______ ．

Given the function f (x) = 3sinx + 4cosx, the maximum value of F (x) is______ ．

The function f (x) = 3sinx + 4cosx 5 (35sinx + 45cosx), let cos θ = 35, sin θ = 45, θ ∈ [0, 2 π]. Then f (x) = 5sin (x + θ) can be obtained from the auxiliary angle formula. According to the range of sine function, the maximum value of F (x) is 5, so the answer is: 5

The maximum value of function f (x) = (3sinx-4cosx) cosx is?

f(x)=(3sinx-4cosx)cosx=3sinxcosx-4(cosx)^2
=3/2six2x-2cos2x-2
=5/2sin(2x-φ)-2
The maximum value is 5 / 2-2 = 1 / 2

What is the maximum value of the function f (x) = 3sinx-4cosx?

f（x）=3sinx-4cosx=5sin(x-φ)
tanφ=4/3
sin(x-φ)

The maximum value of the function y = 3sinx-4cosx is
A change 5 b 5 C 7 D1

y=3sinx-4cosx=5sin(x-θ)
Where Tan θ = 4 / 3
So the maximum is 5
Choose B
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