It is known that the minimum positive period of the function f (x) = cos ω x-sin ω X-1 (ω > 0) is π / 2

f(x)=cosωx-sinωx-1
=√2cos(wx+π/4)-1
(1) T = 2 π / w = π / 2, w = 4
2kπ-π

If sin α ^ 2 + sin β ^ 2 + sin γ ^ 2 = 1, then the maximum value of cos α cos β cos γ is equal to 1

Let x = cos α, y = cos β, z = cos γ, then 1 = (sin α) ^ 2 + (sin β) ^ 2 + (sin γ) ^ 2 = (1 - x ^ 2) + (1 - y ^ 2) + (1 - Z ^ 2) = 3 - (x ^ 2 + y ^ 2 + Z ^ 2), so x ^ 2 + y ^ 2 + Z ^ 2 = 2

Given the vector a = (sin θ, 1), B = (1, cos θ), - π / 2 < θ < π / 2 (1) if a ⊥ B, find θ (2) and find the maximum value of | a + B |

a⊥b =>
a • b = (sinθ) * 1 + 1 * sinθ =0
>
sinθ = cosθ
Also - π / 2
a+b= ( sin(π/4) +1 ,1+cos(π/4))
|a+b|= √{[sin(π/4)+1]^2 + [1+cos(π/4)]^2}
= 1+√2

Given the vector a = (1, sin θ) and vector b = (1, cos θ), what is the maximum value of | vector a-vector B |?

Given the vector a = (sin θ, 1), B = (1, cos θ), - π / 2 < θ < π / 2. Find the maximum value of | a + B |

|a+b|²=(sinθ+1)²+(1+cosθ)²=sin²θ+2sinθ+1+cos²θ+2cosθ+1
=3+2(sinθ+cosθ)=3+2√2sin( θ+π/4)
|a+b|≤√（3+2√2）=1+√2

Given the vector a = (sin θ, √ 3), B = (1, cos θ), - π / 2

A + B = (1 + sin θ, √ 3 + cos θ), length = √ ((1 + sin θ) + (√ 3 + cos θ) = √ (5 + 2Sin θ + 2 √ 3cos θ). If t = 5 + 2Sin θ + 2 √ 3cos θ, the maximum value of the length of a + B is the maximum value of T, t = 5 + 4 (1 / 2 × sin θ + √ 3 / 2 × cos θ) = 5 + 4 (cos60 degrees)

Given vector a = (1,2), vector b = (- 3,2), find: What is the value of K (1) K vector a + vector B is perpendicular to vector A-3 vector B? (2) Is the K vector a + vector b parallel to the vector A-3 vector B? Is it in the same direction or in the opposite direction

(1)
(ka+b).(a-3b)=0
k|a|^2-3|b|^2 +(1-3k)a.b=0
5k-3(13)+(1-3k)(-3+4) =0
2k-38=0
k=19
(2)
(ka+b) //a-3b
=>ka+b = m(a-3b)
=> k= m and 1=-3m
=>k=-1/3
They are the opposite

Let 0 ≤ θ ≤ 2 π, given two vectors OP1 = (COS θ, sin θ), op2 = (2 + sin θ, 2-cos θ), then the maximum length of vector p1p2 is

P1P2=OP2-OP1=(2+sinθ-cosθ,2-cosθ-sinθ)
|P1P2|^2=(2+sinθ-cosθ)^2+(2-cosθ-sinθ)^2
=2 (2-cos θ) ^ 2 + 2 (sin θ) ^ 2 = 10-8cos θ, when cos θ = - 1, take the maximum
The maximum length of p1p2 is √ 18 = 3 √ 2

Set vector a＝(1，0)， If B = (sin θ, cos θ), 0 ≤ θ ≤ π, then| A+ The maximum value of b|is___ .

A kind of
A| = 1 because|
B| = 1, so|
A+
b|2=
A2+
b2+2
a•
b=2+2sinθ
Because 0 ≤ θ ≤ π, so 0 ≤ sin θ ≤ 1, so 2 + 2Sin θ ≤ 4|
A+
b|≤2
So the answer is: 2

1. Let a = (1,0), B = (COS θ, sin θ), where 0 ≤ θ ≤ π, then the maximum value of | A-B | is_____ . Two 2. Given n ∈ Z, in the following trigonometric functions, the same value as sin is () ①sin(nπ+);②cos(2nπ+);③sin(2nπ+);④cos［(2n+1)π-］; ⑤sin［(2n+1)π-］. A.①② B.①③④ C.②③⑤ D.①③⑤

There is no correct answer to question 2
One
|a-b|^2=(a-b) dot (a-b)=|a|^2+|b|^2-2(a dot b)=1+1-2cosθ=2-2cosθ
When cos θ = - 1, the maximum value of | A-B | is 2
Two
When n = 2K, sin (n π + θ) = sin (2k π + θ) = sin θ
When n = 2K + 1, sin (n π + θ) = sin (2k π + π + θ) = sin (π + θ) = - sin θ
cos(2nπ+θ)=cosθ
sin(2nπ+θ)=sinθ
cos((2n+1)π-θ)=cos(π-θ)=-cosθ
sin((2n+1)π-θ)=sin(π-θ)=sinθ
Therefore, only ③ and ⑤ meet the conditions, there is no correct answer

It is known that the minimum positive period of the function f (x) = cos ω x-sin ω X-1 (ω > 0) is π / 2