If f (x) = SiNx cos2x x ∈ (π / 6,5 π / 6], then f (x) range

If f (x) = SiNx cos2x x ∈ (π / 6,5 π / 6], then f (x) range

F (x) = sinx-cos2x = SiNx - (1-2sinx) = 2sinx + sinx-1, because x belongs to (PAI / 6,5pai / 6], so when SiNx = 1, the maximum value of function is f (x) = 2, when x = 5pai / 6, the minimum value of function is f (x) = 0, so the range of function is [0,2]

Point P coordinates (sin θ - cos θ, Tan θ), P is in the first quadrant, and the definition domain of θ is ∈ [0,2 π], and the value range of θ is calculated

P (sin a-cos a, Tan a) is in the first quadrant
So Sina cosa > 0
tana>0
sina-cosa>0
sina>cosa
If cosa > 0, then 3 π / 2

F (θ) = [sin (3 π - θ) cos (π / 2 + θ)] / Tan (π - θ) find the definition domain of ① f (θ) and simplify the expression of F (θ)
③ If f (θ) = 1 / 2, find Tan θ sin θ cos θ

f(θ)=[sin(3π-θ)cos(π/2+θ)]/tan(π-θ)＝sinθcos(π/2－θ)/tanθ＝sin²θ/tanθ
(1) Tan θ ≠ 0 ≠ θ ≠ K π and θ ≠ K π + π / 2
(2)f(θ)＝sin²θ/tanθ＝sinθcosθ＝1/2 sin2θ
(3))f(θ)＝1/2 ∴sin2θ＝1 ∴2θ＝2kπ＋π/2 ∴θ＝kπ＋π/4
∴tanθ＝tan(kπ＋π/4)＝tan(π/4)＝1
sinθ＝sin(kπ＋π/4)＝±√2/2
cosθ＝cos(kπ＋π/4)＝±√2/2

Exponential function, logarithmic function, y = SiN x, y = cos x, y = Tan X domain

1. Exponential function: negative infinity to positive infinity
2. Logarithmic function: 0 to positive infinity, left open interval
3. The domain is r
4. The domain is r
5. ｛ X! X is not equal to K school + Half school, K belongs to Z}

When Xiao Li calculates the addition of three fractions, she uses the method of rounding to get the approximate value a / 3 + B / 7 + C / 12, which is about 1.04

a/3+b/7+c/12≈1.04
1.035≤a/3+b/7+c/12≤1.044
That is 86.940 ≤ 28a + 12b + 7C ≤ 87.696
Yizhi 28a + 12b + 7C = 87
1)a=0,b=2,c=9
2)a=1,b=2,c=5
3)a=2,b=2,c=1
Because 28a and 12b are even and 87 is odd, 7C is odd, so C is odd
28a+12b≥28*0+12*1=12
87=28a+12b+7c≥12+7c
C ≤ 10, C is 1,3,5,7,9
And 87 and 12b are multiples of 3, so 28a + 7C is a multiple of 3, 28a + 7C = 7 * (4a + C), so 4A + C is a multiple of 3

It took 40 seconds for a train to pass through a 440 meter tunnel, and 30 seconds for a train to enter a 310 meter tunnel at the same speed

The length of the train is x meters
（440+x）÷40=（310+x）÷30
x=80
A: the train is 80 meters long
Speed: (440 + 80) △ 40 = 13

Cut a circle into several equal parts along its radius, and then put it together into an approximate rectangle. The perimeter of the rectangle is 49.68 cm. What is the area of the circle?
Use simple formulas, not formulas

1. After putting together an approximate rectangle, the two lengths of the rectangle together are the circumference of the circle, and the width is the radius of the circle
2. So, with the following equation, we can find the radius
2×3.14×r＋2×r=49.68
6.28r＋2r=49.68
8.28r=49.68
r=6
3. Area of circle: 3.14 × 6 × 6 = 113.04 (square centimeter)

The N + 1 power of X - what is the n power of 3x + the n minus 1 power of 2x

=N minus 1 power of X * (x ^ 2-3x + 2)
=N minus 1 power of X * (x-1) * (X-2)

In the chapter of one yuan one time equation, we have considered the following two mobile phone billing methods: the monthly rent is 10 yuan / month, and the local call fee is 0.15 yuan / minute
When the function method is used to solve the call time, the cost of the two charging methods is equal
The second way is 0.20 yuan / min, which is wrong

Set the call time to X minutes
Mode 1: 10 + 0.15x
Mode 2 charge: 0.2x
If the two charging methods are equal, then 10 + 0.15x = 0.2x
The solution is x = 200

In trapezoidal ABCD, M is a point DM on BC, CM bisects angle ADC and angle BCD respectively

After M, me / / AD is transferred to e, and MF / / BC is transferred to F, because AB / / CD
So: if both ADEM and mfcb are parallelograms, then am = De, MB = CF
DM and cm split angle ADC and BCD equally
It can be seen that: angle EMD = angle ADM = angle EDM, angle FMC = angle BCM = angle FCM
It is known that EM = de = am = ad, MF = CF = MB = BC
If ladder ABCD is isosceles ladder, then am = ad = BC = MB
It is known that M is the midpoint of ab