N-fold angle formula of trigonometric function

N-fold angle formula of trigonometric function

N-fold angle formula:
　　sin(nα)=ncos^(n-1)α·sinα-C(n,3)cos^(n-3)α·sin^3α+C(n,5)cos^(n-5)α·sin^5α-…
　　cos(nα)=cos^nα-C(n,2)cos^(n-2)α·sin^2α+C(n,4)cos^(n-4)α·sin^4α-…

What is the angle doubling formula of trigonometric function?

sin2x=2sinxcosx
cos2x=2cosx^2-1=1-2sinx^2=cosx^2-sinx^2
sin3θ＝3sinθ－4sinθ^3 ＝4sinθsin（60°－θ）sin（60°－θ） cos3θ＝4cosθ^3－3cosθ＝4cosθcos（60°－θ）cos（60°＋θ）

Trigonometric function image transformation f(x)=sin(2x+4/π） Shift 6 / π units to the right, and then extend the abscissa of each point in the image to 4 times of the original How does the title change

In this paper, we must pay attention to the problem of transformation: shift x to the left and right, that is, change x into x + A or x-a, pay attention to the transformation must be x, don't take the coefficient, y does not change

How to change trigonometric function image transformation

Left and right translation remember: left plus right minus, that is, if you shift to the left, a few units will change X in the original formula into x plus several units. If you move to the right, all x in the original formula will be changed into x-several units. If you move up, add a few units to y in the original formula, and move down is to subtract several units from y. for example, y or F (x) = SiNx + cos2x-2 shifts two units to the left, It becomes a new function: y = sin (x + 2) + cos (x + 2) - 2, and then move up 2 units? Just add 2 to the formula, that is, y = sin (x + 2) + cos (x + 2) - 2
y=sin(x+2)+cos(x+2)-2+2=sin(x+2)+cos(x+2）

Image transformation of mathematical trigonometric function From cos2x to sin (2x - π / 6). Thank you

Cos2x, shift π / 4 to the right, get Cos2 (x - π / 4) = simplify = sin (2x), and then shift π / 12 to the right to get sin2 (x - π / 12) = sin (2x - π / 6)

The function y = 2cos (π 3x+1 2) How to transform the image of y = cosx?

The function y = 2cos (π
3x+1
2) Shift the image of 3 to the right
2 π units, the function y = 2cos [π
3（x-3
2π）+1
2）=2cosπ
3x image;
Then the abscissa of the point on the obtained image is changed to the original 3
The image of y = 2cosx can be obtained by π times;
Then the ordinate of the image point is changed to the original 1
2 times, the image of y = cosx can be obtained

5. In the function y = asin (ω x + φ), what changes do a, ω, and φ regulate the function image respectively?

A amplitude
ω frequency
φ phase

How to calculate a in function y = asin (ω x + ψ)? Is a the maximum minus the minimum divided by 2? What about the other two? Please give reasons

For example, the function y = asin (ω x + ψ) (a > 0, ω > 0, ψ = 0, the minimum value is - 2, so a = 2 is the highest point and the lowest point in the image

Function y = asin (ω x + ψ), introduce ω, ψ

A, the amplitude of the image changes
2 π / ω is exactly the period, W is the period changing
ψ is the length of forward translation of sin X image

The function of y = asin (ω x + φ) knows a and ω x, how to find φ

Can be replaced by the maximum value point, if the x-axis point, there may be multiple answers