Senior one mathematics (sine cosine function) The function f (x) = sin (x - π / 6), given α, β∈ (0, π / 2), and f (α) = 3 / 5, f (β) = 12 / 13, find the value of F (α - β)

Senior one mathematics (sine cosine function) The function f (x) = sin (x - π / 6), given α, β∈ (0, π / 2), and f (α) = 3 / 5, f (β) = 12 / 13, find the value of F (α - β)

The easiest way to do this is to calculate
f(α)=sin(α-π/6)=sinαcosπ/6-cosαsinπ/6
sinα^2+cosα^2=1
Calculate sin α cos α sin β cos β
Substituting f (α - β)

To change 2Sin (2x + b) into the name of cosine function, the book directly adds a half school after B, but isn't this a period first and then a translation? Shouldn't 2 be put forward and then added after x But only one can be adopted, and the other two are sorry. Hughsks looked at the title in reverse, but it's OK. I understand it

You're right
Let's first look at how SiNx becomes a function of COS
From the function graph, we can know that if cosx is shifted to the right by 1 / 4 period, that is, π / 2 becomes the same function as SiNx, SiNx = cos (x - π / 2)
2Sin (2x + b) is to shift SiNx to the left by B units, then reduce the period, and stretch up and down. In other words, first reduce the period to π, then shift B / 2 to the left, and finally stretch up and down
In short, whether it is translation or periodicity, the result is the same, but the statement is different, that is, you have to find a way to change the sine function into a cosine function which is equal to it
In your opinion:
We can see that the period of 2Sin (2x + b) is π, and raising 2 is 2Sin [2 (x + B / 2)], which is equivalent to reducing SiNx period to π, then shifting B / 2 units to the left, and then stretching up and down. Cos (2x + B) also changes in the same way, while the difference between COS (2x + b) and sin (2x + b) is 1 / 4 cycle difference. As long as cos (2x + b) is shifted to the right by 1 / 4 cycle, that is to say, by subtracting π / 4 from X, it becomes
Cos [2 (x - π / 4) + b] is cos (2x + B - π / 2)
okay?
How can I subtract π / 2? Am I wrong or is the book wrong?

The symmetry axes of the function y = sin (2x + Π / 3) are respectively If the image of the function f (x) = SiNx + 2 / SiNx /, x [0,2 Π] has and only two different intersections with the line y = k, then the value range of K is

The first question is that the sin (x) axis of symmetry is k π + 4 / π, the center of symmetry is (K π / 2,0) sin (x + 6 / π) is the left translation π / 6 unit symmetry axis, that is k π + π / 12 symmetry center is (k π / 2 - 6 / π, 0) the answer is sin (2x + Π / 3) symmetry axis, that is, K π / 2 + π / 12 symmetry center is (K π / 4 - 6 / π, 0

How to define sine function, cosine function and tangent function of any angle?

Let the terminal edge of any angle α intersect the circle with radius r at the point (x, y), and √ (x ^ 2 + y ^ 2) = R > 0, then
sinα=y/r
cosα=x/r
tanα=y/x
They are called sine, cosine and tangent of α
These ratios are functions of angles as independent variables
They are called sine function, cosine function and tangent function respectively

How to find the value of cosine function and tangent function when the value of a sine function is known? How to find the value of sine function and tangent function when the value of a sine function is known? How to calculate the value of sine function and cosine function when the value of a tangent function is known?

From Sina squared + cosa squared = 1
Cosine can be found
Then divide the sine by the cosine to get the tangent
If it is junior high school mathematics, then these three values are positive

Symmetry axis and point coordinates of sine function, cosine function and tangent function

X = k beat + beat / 2; X = k beat (k belongs to positive integer); origin

How does the period of sine function cosine function tangent function change after square?

The period becomes half of the original
cosx^2=(1+cos2x)/2
sinx^2=(1-cos2x)2

Cosine function image and its properties*

1、 The image and properties of trigonometric function
sinx=
cosx=
tanx=
cotx=
The domain x ∈ R x ∈ R {x | x ≠ K π +, K ∈ Z}
{x|x≠kπ,k∈Z}
Range [- 1,1] [- 1,1] (- ∞, + ∞) (- ∞, + ∞)
image
Parity odd function even function odd function odd function odd function
Monotone monotone increasing interval [2K π -, 2K π +] K ∈ Z
Monotone decreasing interval [2K π +, 2K π +] K ∈ Z monotone increasing interval
[2kπ-π,2kπ]k∈Z
Monotone decreasing interval
Increasing π π∈π∈2k
(kπ- ,kπ+ ), k∈Z
Monotone decreasing interval
(kπ,kπ+π)k∈Z
Periodicity t = 2 π t = 2 π t = π t = π t
Symmetry center of symmetry:
(kπ,0) k∈Z
Axis of symmetry:
x=kπ+ ,k∈Z
Center of symmetry:
(kπ+ ,0)k∈Z
Axis of symmetry: x = k π, K ∈ Z, center of symmetry: (, 0)
Center of symmetry: (, 0)
When the maximum value x = 2K π +, the maximum value of Y is 1;
When x = 2K π + π, y takes the minimum value - 1; when k ∈ Z x = 2K π, y takes the maximum value of 1;
When x = 2K π + π, the minimum value of Y is - 1; K ∈ Z is nonexistent
2、 Images and properties of the function y = asin (ω x +) (a > 0, ω > 0)
1. Image
The image of the function y = asin (ω x +) (a > 0, ω > 0) x ∈ R can be obtained by transforming the image of y = SiNx in the following order:
① Phase transformation: all points on the y = SiNx image are left (> 0) or right (1) or elongated (0)

The image and properties of cosine function If the function f (x) = 2cos (3x + FAI) is an odd function and Fai ∈ (0, π), then FAI= Forgive me for not being able to type this symbol

F (0) = 0
π/2

Find sine, cosine function formula! Who can help the sine, cosine formula, trigonometric function and so on, anyway is high school and angle related formula to me to summarize, write down!

The induction formula sin (- a) = - sin (a) cos (a) cos (- a) = cos (a) a) sin (2 π - a) = cos (a) cos (a) cos (2 π - a) = cos (a) cos (2 π - A) = sin (a) sin (2 π + a) = cos (a) cos (2 π + a) = - sin (a) sin (a) sin (π - a) = sin (a) cos (π - a) = - cos (a) sin (a) sin (π + a) = - sin (a) cos (π + a) = - cos (π + a) = - cos (a) TG a = Tana = Tana = Sina = Tana = Tana = Sina = Sina = Sina = Sina = Sina = a = Sina = sinsinsinand