What is the minimum positive period of the function y = sin (4th power) x + cos (4th power) x?

What is the minimum positive period of the function y = sin (4th power) x + cos (4th power) x?

Y = (SiNx) ^ 4 + (cosx) ^ 4 = [(SiNx) ^ 2 + (cosx) ^ 2] ^ 2-2 (SiNx) ^ 2 (cosx) ^ 2 = 1 - (1 / 2) [sin (2x)] ^ 2 = 1 - (1 / 4) 2 [sin (2x)] ^ 2 = 1 / 4 - (1 / 4) 2 [sin (2x)] ^ 2 + 3 / 4 = (1 / 4) {1-2 [sin (2x)] ^ 2} + 3 / 4 = (1 / 4) cos (4x) + 3 / 4, then the minimum positive period T = 2 π / 4 = π / 2

The period of the function y = sin to the fourth power X + COS to the fourth power X is A,π/2 B,π C,2π D,4π

c

What is the period of the function y = COS to the fourth power x-sin to the fourth power X? When x =? When, y has a minimum value of - 1

y=cos^4x-sin^4x=(cos ² x-sin ² x)(cos ² x+sin ² x)=cos2x × 1=cos2x
So the period of this function is: T = 2 π / 2 = π
Let y = - 1, cos2x = - 1
2x=π+2kπ
x=(π/2)+kπ
That is, when x = (π / 2) + K π, y = - 1

To get the image of the function y = sin (4th power) x-cos (4th power) x, just change the function y = 2sincos?

Let's use a ^ B to represent the B power of A. = = = = = = because (SiN x) ^ 4 - (COS x) ^ 4 = [(SiN x) ^ 2 + (COS x) ^ 2] [(SiN x) ^ 2 - (COS x) ^ 2] = - cos 2x = sin (2x - π / 2) = sin 2 (x - π / 4), and because 2 SiN x cos x = sin 2x, we want to get y

The interval of the zero point of the function f (x) = e to the power of X + X-2 is A（-2,-1） B(-1,0) C(0,1) D(1,2)

Choose C
After calculation, f (- 2) = -3.864

Find the zero point of function f (x) = 2x cubic - 3x + 1

f(x)=2x^3-3x+1=2x^3-2x^2+2x^2-2x-x+1=(x-1)(2x^2+2x-1)
Therefore, the zero point is: x = 1, (- 1 + √ 3) / 2, (- 1 - √ 3) / 2