PI represents the multiple relationship of circle () and () with two decimal places reserved Yes, I'll take it. I'll add another 50

PI represents the multiple relationship of circle () and () with two decimal places reserved Yes, I'll take it. I'll add another 50

The PI represents the multiple relationship between the circumference and diameter of a circle, with two decimal places being 3.14

The function f (x) = SiNx cos (x + π) 6) The value range of is () A. [-2，2] B. [- 3， 3] C. [-1，1] D. [- Three 2， Three 2]

The function f (x) = SiNx cos (x + π)
6）=sinx-
Three
2cosx+1
2sinx
= -
Three
2cosx+3
2sinx
=
3sin（x-π
6）∈[−
3，
3]．
Therefore, B

Why is the value range of function f (x) = SiNx cos (x + π / 6) [- √ 3, √ 3]?

0

0

y=(1-sin²x)-sinx
=-sin²x-sinx+1
=-(sinx+1/2)²+5/4
-1

The value range of the function y = cos ^ 2 x - SiNx is?

Y=COS²X-SINX
=1-SIN²X-SINX
=-（SINX+1/2）²+5/4
Because - (SiNx + 1 / 2) 2 ≤ 0, the maximum value of the function is 5 / 4 when SiNx = - 1 / 2
The maximum absolute value of SiNx + 1 / 2 is 3 / 2 of SiNx = 1, so the minimum value of function is - (3 / 2) 2 + 5 / 4 = - 1
Therefore, the range is 〔 - 1,5 / 4]

Find the value range of the function y = cos ^ 2 x-sinx

y＝cos^2 x-sinx
=1-sin²x-sinx
=-(sinx+1/2)²+5/4
therefore
When SiNx = - 1 / 2, there is
Max = 5 / 4
When SiNx = 1, there is
Minimum = 1-1-1 = - 1
The range is: [- 1,5 / 4]

What is the value range of the function y = cos (x + 5 °) + 3 √ 2 cos (x + 50 °)?

y=cos(x+5°)+3√2 cos(x+50°)=cos(x+5°)+3√2 cos(x+5°+45°)=cos(x+5°)+3√2 [cos(x+5°)cos45°-sin(x+5°)sin45°]=cos(x+5°)+3 [cos(x+5°)-sin(x+5°)]=4cos(x+5°)-3sin(x+5°)=5[4/5*cos(x+5°)-3/5*si...

If the odd function f (x) defined on R satisfies f (x-4) = - f (x) and is an increasing function on the interval [0,2], then () I want to ask is, in the process of solving the problem, the given condition will be changed into f (X-8) = f (x) with 8 as the cycle function can not be directly used to calculate the function with 4 as the cycle? In addition, why use the given number divided by 8, the remaining number is x in F (x)?

A: No, because f (x-4) = - f (x), 4 is not a period. If the period is 8, if f (9) = f (9) = f (1) and f (17) = f (17-8) = f (9) = f (1), 1 is 17

It is known that the odd function y = f (x) defined on R satisfies f (x-4) = - f (x), and the interval [0,2] is an increasing function A.f(-25)＜f(11)＜f(80) B.f(80)＜f(11)＜f(-25) C.f(11)＜f(80)＜f(-25) D.f(-25)＜f(80)＜f(11)

f(x+8)=-f(x+4)=f(x)
So the period is 8
So:
f(-25)=f(-1)
f(80)=f(0)
f(11)=f(3)=-f(-1）=f(1)
Because f (x) is an odd function and an increasing function on the interval [0,2]
So f (x) is an increasing function on [- 2,2]
So f (- 1)

Let f (x) = sin (x + a) + cos (x + a) be defined in R (1). When a = 0, find the monotone increasing interval of F (x) (2) If a belongs to (0, π) and sina is not equal to 0, then f (x) is an even function

(1) When a = 0,
f(x)=sinx+cosx
=√2sin(x+π/4)
2kπ-π/2