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If the amplitude of the function y = asin (Wx + φ) (a > 0, w > 0) is 3, the minimum positive period is 2 π / 7, and the initial phase is π / 6, then its analytical expression? Value range is? 6. The symmetry axis of the function y = sin (2x + 5 π / 2)? Minus interval? 7. The image with y = cos (x + 4 π / 3) is shifted to the right by? Units, and the image obtained is symmetrical about the y-axis? 8. The image of the function y = asin (Wx + φ) (a > 0, w > 0) has a highest point (π / 12,2) and a lowest point (7 π / 12, - 2) in the same period?
According to w = 2 π / T, w = 7, φ = π / 6, so the analytic formula is y = 3sin (7x + π / 6). 6. According to the symmetry axis of SiNx is π / 2 + K π, π / 2 + K π = 2x + 5 π / 2, so the axis of symmetry is x = - π + K π / 2, SiNx minus interval is [π / 2 + 2K π, 3 π / 2 + 2K π]
The fourth power of the function y = 4cos + the fourth power of 4sin - 3 is the form of y = asin (Wx + φ). What are the amplitude, period, initial phase and range of values
As for the period, the value range is (- 1,1). I don't know whether it is right or not. The calculation process is as follows: y = 4 * (cosx) ^ 4 + 4 * (SiNx) ^ 4-3 = (1 + cos2x) ^ 2 + (1-cos2x) ^ 2-3 = 1 + 2 * cos2x + (cos2x) ^
Seeking mathematical formula of senior one
Trigonometric function formula
Sum of two angles formula
sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB) tan(A-B)=(tanA-tanB)/(1+tanAtanB)
ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA) ctg(A-B)=(ctgActgB+1)/(ctgB-ctgA)
Double angle formula
tan2A=2tanA/(1-tan2A) ctg2A=(ctg2A-1)/2ctga
cos2a=cos2a-sin2a=2cos2a-1=1-2sin2a
Half angle formula
sin(A/2)=√((1-cosA)/2) sin(A/2)=-√((1-cosA)/2)
cos(A/2)=√((1+cosA)/2) cos(A/2)=-√((1+cosA)/2)
tan(A/2)=√((1-cosA)/((1+cosA)) tan(A/2)=-√((1-cosA)/((1+cosA))
ctg(A/2)=√((1+cosA)/((1-cosA)) ctg(A/2)=-√((1+cosA)/((1-cosA))
Sum difference product
2sinAcosB=sin(A+B)+sin(A-B) 2cosAsinB=sin(A+B)-sin(A-B)
2cosAcosB=cos(A+B)-sin(A-B) -2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB=2sin((A+B)/2)cos((A-B)/2 cosA+cosB=2cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB tanA-tanB=sin(A-B)/cosAcosB
ctgA+ctgBsin(A+B)/sinAsinB -ctgA+ctgBsin(A+B)/sinAsinB
Sum of the first n terms of some sequences
1+2+3+4+5+6+7+8+9+… +n=n(n+1)/2 1+3+5+7+9+11+13+15+… +(2n-1)=n2
2+4+6+8+10+12+14+… +(2n)=n(n+1) 12+22+32+42+52+62+72+82+… +n2=n(n+1)(2n+1)/6
13+23+33+43+53+63+… n3=n2(n+1)2/4 1*2+2*3+3*4+4*5+5*6+6*7+… +n(n+1)=n(n+1)(n+2)/3
Sine theorem a / Sina = B / SINB = C / sinc = 2R note: where R is the circumscribed radius of a triangle
Cosine theorem B2 = A2 + c2-2accosb note: angle B is the angle between edge a and edge C
The arc length formula L = a * r a is the radian number of the central angle R > 0, and the fan area formula s = 1 / 2 * L * r
Multiplication and factorization A2-B2 = (a + b) (a-b) A3 + B3 = (a + b) (a2-ab + B2) a3-b3 = (a-b (A2 + AB + B2)
Trigonometric inequality | a + B | | a | + | B | A-B | ≤| a | + | B | a | ≤ B-B ≤ a ≤ B
|a-b|≥|a|-|b| -|a|≤a≤|a|
Solutions of quadratic equation of one variable - B + √ (b2-4ac) / 2A - B - √ (b2-4ac) / 2A
The relation between root and coefficient X1 + x2 = - B / a X1 * x2 = C / a note: Weida theorem
Discriminant
B2-4ac = 0 note: the equation has two equal real roots
B2-4ac > 0 note: the equation has two unequal real roots
b2-4ac
All the formulas of senior one mathematics
Trigonometric function formula sum formula sin (a + b) = sinacosb + cosasinb sin (a-b) = sinacosb sinbcos a cos (a + b) = cosacosb sinasinb cos (a-b) = cosacosb + sinasinb Tan (a + b) = (Tana + tanb) / (1-tanatanb) Tan (a-b) = (Tana tanb) / (1 + tanatanb)
Seeking the formula of mathematics in senior one
A ^ 2-B ^ 2 = (a + b) (a-b) a ^ 3 + B ^ 3 = (a + b) (a-b) a ^ 3 + B ^ 3 = (a + b) (a ^ 2-AB + B ^ 2) < A ^ 3-B ^ 3 = (a-b (a ^ 2 + AB + B ^ 2) triangle inequality | a + B | | a + B | | a | a | B | A-B | A-B | a | a || a | a || B | B | a | a | a | a | a | a solutionsof quadratic equation of one variable - B + √ (b
What is the mathematical frequency formula of senior one
Frequency = frequency / total
Let the minimum value of function f (x) = x2-2x + 2, X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
F (x) = x2-2x + 2 = (x-1) 2 + 1, so the symmetry axis of the image is a straight line x = 1, and the opening of the image is upward. ① when t + 1 < 1, that is, T < 0, f (x) is a decreasing function on [T, t + 1], so g (T) = f (T + 1) = T2 + 1; ② when t ≤ 1 ≤ T + 1, i.e. 0 ≤ t ≤ 1, the function f (x) is obtained at the vertex
The maximum value of the function y = asin (Wx Φ) B is 5, the minimum value is - 1, and its amplitude is?
The maximum distance of a vibrating object from its equilibrium position is called the amplitude of vibration
The maximum value is 5, the minimum value is - 1, the vibration amplitude is 3, and the equilibrium position is 2
If the maximum value of the function asin (3x - π / 6) + B (a, B are constants, and a > b) is - 1, the amplitude, period, initial phase and frequency are calculated If the maximum value of the function asin (3x - π / 6) + B (a, B are constants, and a > b) is - 1, the amplitude, period, initial phase, frequency and correct second batch are obtained
A+B=5
B-A=-1
A=3 B=2
Amplitude 3
Period 2 π
Primary phase - π / 6
Frequency = reciprocal of period = 3 / 2 π
Find the maximum and minimum value of the function y = 2sin2x + 2cosx-3, and obtain the set of maximum and minimum value of X
Is sin2x in y = 2sin2x + 2cosx-3 the square of SiNx?
y=2(sinx)^2+2cosx-3=-2(cosx)^2+2cosx-1=-2(cosx-1/2)^2-1/2
When cosx = 1 / 2, the function has the maximum value: - 1 / 2, where x = 2K π + π / 3, x = 2K π - π / 3; (k is an integer)
When cosx = - 1, the function has the minimum value: - 5, where x = (2k + 1) π. (k is an integer)
If sin 2x in y = 2sin2x + 2cosx-3 is the sine of 2x, then we need to find the derivation
RELATED INFORMATIONS
- 1. How to learn the properties of the function y = asin (Wx + φ)? It feels so difficult
- 2. Compulsory exercise 1.2b group 1~
- 3. Find the area of the plane figure enclosed by the square of the curve y = 4-x, y = the square of X - 2x Specific process, thank you!
- 4. Find the area of the plane figure surrounded by the curve y = x and y = X
- 5. If the image of function y = SiNx is symmetric about y-axis, the image obtained is shifted to the left by π / 4 unit length. The analytic expression of the image obtained is ()
- 6. If cosx + cosy = 1 / 2, SiNx siny = 1 / 3, then cos (x + y) =?
- 7. Find the value range and minimum positive period of the function f (x) = 2cos (x + PIA / 4) cos (x-pia / 4) + root sign 3sin2x
- 8. Known function f (x) = 5 root 3cos square x + root 3sin square x-4sinxcosx (1) When x belongs to real genus, find the minimum value of F (x) (2) If π / 4 ≤ x ≤ 7 π / 24, find the monotone interval of F (x)
- 9. It is known that f (x) = 2sinxcosx + 2 root sign 3cos square x-1-radical 3 (2) Find out the symmetry center coordinate and symmetry axis equation of curve f (x) (1) When x belongs to [0. π / 2], find the maximum value of F (x) and the value of X at this time. (3) Find the monotone increasing interval of F (x) on which X belongs to [- 2 / π, 2 / π]. (4) Put the f (x) image to enjoy translation unit after. The resulting image is symmetric about the y-axis. Find the minimum value of M. (5) When x belongs to [0, π], find the x value of F (x) = 0. (6) This paper explains how to get the image of function f (x) from the image of y = SiNx.
- 10. The minimum value and minimum positive period of the function FX = sinxcosx are
- 11. Given the function f (x) = asin (Wx + φ) (a > 0, | φ | π / 2, w > 0), find the analytic formula of F (x), as shown in Fig
- 12. The known function y = asin (ω x + φ), |φ|
- 13. The known function f (x) = 2Sin 2 (π / 4 + x) -√ 3 cos2x-1, X ∈ R (1) If the image of the function H (x) = f (x + T) is symmetric about the point (- π / 6,0), and t belongs to (0, π), the value of T is? (2) Let P: X ∈ [π / 4, π / 2], q; M-3 < f (x) < m + 3, if P is a sufficient and unnecessary condition of Q, the value range of real number m is obtained The first question t has two answers, and I remember one of them is π / 3
- 14. Given that the line x = π / 6) is a symmetric axis of the image of the function y = asinx bcosx, then what is the symmetry axis of the image of the function y = bsinx + acosx?
- 15. Reduction function f (x) = cos2x / sin (45 '- x)
- 16. It is proved that: (1 + cot? α) / (1-cot? α) = 1 / (2Sin? α - 1) urgent!
- 17. F (x) is an even function defined on R when x
- 18. If an even function defined on R is an increasing function on [0, positive infinity), and f (2) = 1, then the x value range of F (Log1 / 2 x) > 1 is
- 19. If the even function f (x) over the definition field r has f (x) = - f (x + 3 / 2) for any real number x, and f (- 1) = 1, f (0) = - 2, then f (1) + F (2) +... " The value of F (2012) is
- 20. Let f (x) = 2x 2 - 3x + 1, G (x) = asin (x - π / 6), (a ≠ 0) (1) When 0 ≤ x ≤ π / 2, find the maximum value of y = f (SiNx); (2) If for any x 1 ∈ [0,3], there is always x 2 ∈ [0,3], so that f (x1) = g (x2) holds, find the value range of real number a; (3) The equation f (SiNx) = a-SiNx has two solutions on [0,2 π]