The maximum of y = 2Sin (SiNx cosx)

The maximum of y = 2Sin (SiNx cosx)

y=2sin(sinx-cosx)
=2sin²x-2sinxcosx
=(1-cos2x)-sin2x
=1-(sin2x+cos2x)
=1-√2sin(2x+π/4)
So the maximum value is 1 + √ 2

What is the maximum value of the square of y = SiNx minus SiNx + 1, X ∈ r

The maximum value is 3, welcome to inquire
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Find the limit (x → 0) (SiNx TaNx) / (x ^ 2 (e ^ 2x - 1))

Let's use the equivalent infinitesimal: e ^ (2x) - 1 2x primitive = LIM (SiNx - TaNx) / (2x ^ 3) = Lim [cosx - (secx) ^ 2] / 6x ^ 2 [Robida's Law] = Lim [(cosx) ^ 3 - 1] / [6x ^ 2 (cosx) ^ 2] = LIM (cosx - 1) [(cosx) ^ 2 + cosx + 1] / [6x ^ 2 (cosx) ^ 2] = Lim [...]

Mathematics problem ·· find the function y = cos2x + SiNx, X belongs to the range of [quarter π, 5 / 6 π]

y=1-2sin²x+sinx
=-2(sinx-1/4)²+9/8;
∵x∈[π/4,5π/6]
∴sinx∈[1/2,1]
The maximum value is 1;
SiNx = 1, minimum value = 0;
Range bit [0,1]
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F (α) = [sin (π - α) cos (α - π) Tan (- α + π)] / [Tan (π + α) cos (3 / 2 π + α)] reduction

f(α)=[sin(π-α)cos(α-π)tan(-α+π)]/[tan(π+α)cos(3/2π+α)]
=sinα(-cosα)(-tanα)/(tanαsinα)
=cosα

What is the domain? How to find the domain of logarithmic function and the domain of exponential function?

Is the value range of the independent variable x
The definition fields of logarithmic function and exponential function are directly explained by the definition of function, otherwise they are not logarithmic function and exponential function
The domain of logarithmic function is positive real number set, and the domain of exponential function is all real numbers

The range of function y = Tan (2x + π / 4), (- π / 4 ≤ x ≤ π / 4)

y=tan(2x+π/4),
-π/4≤x≤π/4
be
-π/4≤2x+π/4≤3π/4
therefore
The range of Y is (negative infinity, positive infinity)

Explain what is sin, cos, Tan, and why there is a ratio! I'm stupid
I understand, and there are bonus points! I have another question, isn't there two adjacent sides, one long and one short, how to determine which one is!

In the right triangle ABC, ∠ C = 90 ° = = = = = = = = = = = AB is called hypotenuse, AC, BC is called right side; in the right triangle, the longest hypotenuse is = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

With the help of cotan, it's better to have examples

In a right triangle: cos cosine = adjacent / hypotenuse; sin sine = opposite / hypotenuse; Tan tangent = opposite / hypotenuse; cot cotangent = adjacent / hypotenuse; Cos cosine = x / √ (x ^ 2 + y ^ 2); sin sine = Y / √ (x ^ 2 + y ^ 2); Tan sine

Junior three or senior high school certificate, Tan sin cos
It is proved that Tan (x / 2) = (1-cosx) / SiNx

COS2X=1-2COS^2 X
SIN2X=2SINXCOSX
You know, bring it in, and it becomes 2cos ^ 2 (x / 2),
Here is 2Sin (x / 2) cos (x / 2)
And then we get the approximate score