What does "boundedness of sine function and cosine function" mean?

What does "boundedness of sine function and cosine function" mean?

That is, sine function and cosine function range, we can find two numbers m, N, such that m ≤ f (x) ≤ n
The range of sine function is [- 1,1]
The range of cosine function is [- 1,1]

Detailed explanation of the definition domain of sine function and cosine function, If SiNx ≥, cosx ＞ 0, then {x {2} + 2K π ≤ x ＜ π + 2K π}, I want to know the specific steps

∵sinx≥0
The final edge of angle X is in quadrant 1,2 and X axis
Cosx > 0
The final edge of the angle X lies in the quadrant 1,4 and the positive half axis of the X axis
The final edge of angle X is in quadrant 1 and the positive half axis of X axis
The set of angle X is
｛x｜2kπ≤x＜π/2+2kπ,k∈Z｝

The symmetry axis and center of sine cosine tangent function

The symmetry axis of the image with y = SiNx is: x = k π + π / 2; therefore, the symmetry axis of the image with the function y = asin (ω x + ψ) + B is; ω x + ψ = k π + π / 2 are used to calculate: x = k π / ω + π / 2 ω - ψ / ω y = SiNx symmetry center coordinates: (K π, 0) so the function: y = asin (ω x + ψ) + B's image symmetry center coordinates are obtained by analogy: (K π, 0)

The image and properties of cosine function

The maximum value is 1, the minimum value is - 1, and the initial phase of the difference between the sine function and Pai / 2 is wave type. It is symmetrical about the y-axis. The ascending range is 2K * Pai, 2K * Pai, decreasing interval is 2K * Pai, 2K * Pai + Pai, and K is a positive integer
Analytic formula: y = cosx, X belongs to the set of real numbers, and y = cos (x + PAI) = cos (x + 2K * PAI)

In the second semester of senior high school, several formulas for the horizontal throwing motion of Science Physics and mathematical sine cosine function?

1. Velocity: using the rectangular coordinates in the horizontal and vertical directions, we can get: VX = V0, vy = GT, the combined velocity is under the root sign [V0 ^ 2 + (GT) ^ 2] 2. The displacement: x = V0 T, y = (GT ^ 2) / 2 3. The acceleration: ax = 0, ay = g, the natural coordinate an = GCOS θ, a τ = GSIN θ and sin θ = GT / root sign

Sine cosine function Δ ABC, A-B = 4, a + C = 2B, and the maximum angle is 120 degrees?

Given that A-B = 4, a + C = 2B, then: B-C = A-B = 4, then we know that a > b > C is the largest edge of the triangle. Then, from the big side to the large angle, we can get: ∠ a = 120 ° from the cosine theorem: a? = B? + C? - 2BC * cosa = B? + C? - 2BC * cos120? = B? + C? + BC because B = A-4

Sine function image The lowest point of sine function can be expressed as (2k π - π / 2, - 1) Can it be expressed as (2k π + 2 π / 3, - 1)? Is there a difference between the two?

No, its lowest point can be expressed as (2k π - π / 2, - 1) or (2k π + 3 π / 2, - 1) but not (2k π + 2 π / 3, - 1). You can find a value of K. The simplest way is to make K equal to 0, with different initial phases sin (- π / 2) = sin (3 π / 2) = - 1, and sin (2 π / 3) = (root number 3) / 2

What are the characteristics of the image of sine function

Wave shape. Passing through the origin, symmetrical about the origin center, periodic

Image problem of sine function The following figure shows the sine function y = a sin (ω x + φ) (a > 0, ω > 0, |φ)|

0

0

It's better to find the analytic formula first