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If y = sinwx (W > 0) has two maximum values in [0.1], the period of function is calculated
The maximum value occurs twice in [0,1]
The maximum value is Wx = 2K π + π / 2
x=2kπ/w+π/(2w)
Obviously, here K is taken as 0 and 1
So π / (2W) > 0
2π/w+π/(2w)
The minimum positive period of the function y = sinwx is 3 π, and the value of W is obtained
Because
T=2π/|w|
therefore
T=2π/|w|=3π
|w|=2/3
W = - 2 / 3 or 2, 3
If the period of function y = sinwx (W > 0) is 2 / 3 π, then=
2 π / w = t (period)
SO 2 π / w = 2 π / 3
w=3
In order to make the function y = sinwx (W > 0) have at least five minimum positive periods in the interval [0,1], the minimum value of W is obtained
2 π / w * 5 = 10 π,
The minimum value of W is 10 π
The minimum positive period of the function y = 2sin2x is______ ．
Because: y = 2sin2x = 1-cos2x, so: function minimum positive period T = 2 π 2 = π, so the answer: π
The minimum positive period of function y = 1 / 2sin2x ^ 2
y=1/2sin2x^2
=1/2(1-cos4x)
So the minimum positive period of the function y = 1 / 2sin2x ^ 2 is 2 π / 4 = π / 2
The minimum positive period of function y = 2sin2x-3cos2x
RT.
Last time I asked a question, I missed 2
y=2sin2X-3cos2X
=√ 13sin (2x-56.31 degrees)
Minimum positive period T = 2 π / w = 2 π / 1 = π
What is the minimum positive period of the function y = 2sin2x-3cos2x? How to solve it
Asin ω x + bcos ω x = √ (a ^ 2 + B ^ 2) sin (ω x + φ) this formula should remember that the minimum positive period is t = 2 π / ω
The solution to this problem is π
Knowledge of periodic functions
If f (x + a) = - f (x), then its periodic function is ()
F (x + 2a) = f (x) period 2A
It is proved that f (x + 2a) = f (x + A + a) = - f (x + a) = - [- f (x)] = f (x)
For the problem of periodic function, please write out the proof process and find out the period
If x ∈ R, y = f (x) is symmetric with respect to the straight line x = a, x = B (a ≠ b), then f (x) must be a periodic function and 2 (B-A) is the period of y = f (x)
Certification:
The image of the function y = f (x) is symmetric with respect to the line x = a
Then f (x) = f (2a-x)
The image of the function y = f (x) is symmetric with respect to the line x = B
Then f (x) = f (2b-x)
So f (2a-x) = f (2b-x)
Let y = 2b-x
Then f (y) = f [y + 2 (a-b)]
Because y is arbitrary
So f (x) is a periodic function with period 2 (a-b)
The period is 2 (a-b)
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