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Reduction function f (x) = cos2x / sin (45 '- x)
f(x)=cos2x/sin(45°-x)
= (cos^2x-sin^2x)/(sin45°cosx-cos45°sinx)
= (cosx+sinx)(cosx-sinx) / [√2/2(cosx-sinx)]
= √2(cosx+sinx)
= 2(sinxcos45°+cosxsin45°)
= 2sin(x+45°)
It is urgent to simplify logic function with formula method, Simplify logic function with formula method, l = AD + a'd + AB + a'c + BD + ab'ef + b'ef, please help,
L=AD+A'D+AB+A'C+BD+AB'EF+B'EF
L=D+AB+A'C+BD+AB'EF+B'EF
L=D+AB+A'C+AB'EF+B'EF
L=D+AB+A'C+B'EF
Logic function, reduced to the simplest and or expression 1. A (a'c + BD) + B (c + de) + BC 'the answer is B' means not
Aa'c + abd + BC + BDE + BC '
Where aa'c = 0 (complementary law)
BC + BC '= B (associative law, complementary law)
So the formula is simplified to B + abd + BDE = B (1 + AD + de) = B
So the final answer is a (a'c + BD) + B (c + de) + BC '= B
The function y = | X-2 | - | x + 2 |, X is any real number. Simplify the expression of function y
There are two points on the number axis: x = 2 and x = - 2
Between districts
1.x
If the line x = π / 6 is a symmetric axis of the image of the function y = asinx + bcosx, what is the inclination angle of the line ax + by + C = 0
Suppose that tant = B / A, 1 / cost = √ (a ^ 2 + B ^ 2) / A
y=asinx+bcosx
=a(sinx+tantcosx)
=√(a^2+b^2)sin(x+t),x=π/6
x+t=π/2
t=π/3,arctana/b=π/6
The inclination angle of AX + by + C = 0
π-arctan(a/b)=5π/6
Let a symmetric axis equation of the image of the function F X = asinx bcosx be x = π / 4, then the inclination angle of the line ax + by + C = 0 is
From the problem design, for any x ∈ R, there is always f [(π / 2) - x] = f (x). That is, asin [(π / 2) - x] - bcos [(π / 2) - x] = asinx bcosx. = = > acosx bsinx = asinx bcosx. = = > (a + b) (SiNx cosx) = 0. = = > A + B = 0. = = > A = - B. the slope of the line ax + by + C = 0 K = - A / b = 1
If the symmetric axis of the image of the function f (x) = asinx bcosx is a straight line x = π / 4, then a + B = O. the judgment is correct and needs to be analyzed
∵ the function f (x) = asinx bcosx image is x = π / 4
∴f(0)＝ f(π/2)
asin0－bcos0＝asin (π/2)-bcos(π/2)
∴－b＝a
/ / A + B = O is correct
If the line x = Pai / 6 is an axis of symmetry of the image of the function y = asinx + bcosx, then the tilt angle of the line ax + by + C = 0 is?
First of all, by using the formula of one of two, then y = √ a ^ 2 + B ^ 2 sin (x + ψ) Tan ψ = B / A, and ψ and coordinates (a, b) are in the same quadrant
Since the symmetry axis is told to be x = π / 6, the maximum or minimum value of Y is taken when x = π / 6
Let π / 6 + ψ = π / 2, then ψ = π / 3, Tan ψ = √ 3 A / b = √ 3 / 3; when x = π / 6 is the minimum value, Tan ψ = √ 3; then the slope of the straight line is - √ 3 / 3, and the inclination angle of the line is 150 °
Let f (x) = asinx bcosx image be x = π 4, then the inclination angle of the line ax by + C = 0 is () A. π Four B. 3π Four C. π Three D. 2π Three
When x is the axis of symmetry, the value of function is maximum or minimum
That is, a − B
2＝
a2+b2，
The solution is: a + B = 0
Slope k = a
b＝−1，
Ψ the inclination angle of the line ax by + C = 0 is α = 3 π
4．
Therefore, B
If a symmetric axis equation of the function y = asinx-bcosx is x = π / 4, then the inclination angle of the line ax by + C = 0 is? It is analyzed in reference books The analysis of the reference book is: y = √ (a 2 + B 2) * sin (x - α), where Tan α = B / A, then x - α = k π + π / 2 (k belongs to Z). Why X - α = k π + π / 2 is not clear
Consider x-a as a whole, let C = x-a, then y = *The axis of symmetry of sinc, y is C = k paipai / 2. It's troublesome to type on your mobile phone. If you can't find the symbols, you can understand them
RELATED INFORMATIONS
- 1. 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?
- 2. 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
- 3. The known function y = asin (ω x + φ), |φ|
- 4. 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
- 5. 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?
- 6. How to learn the properties of the function y = asin (Wx + φ)? It feels so difficult
- 7. Compulsory exercise 1.2b group 1~
- 8. 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!
- 9. Find the area of the plane figure surrounded by the curve y = x and y = X
- 10. 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 ()
- 11. It is proved that: (1 + cot? α) / (1-cot? α) = 1 / (2Sin? α - 1) urgent!
- 12. F (x) is an even function defined on R when x
- 13. 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
- 14. 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
- 15. 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]
- 16. The function f (x) is defined by π 2 is a periodic even function, and f (π) 3) If = 1, then f (− 17 π) 6)=______ .
- 17. F (x) = (1 + cos2x) sin ^ 3x to find out whether the minimum positive period of a function is odd or even,
- 18. Let the definition domain of F (x) and G (x) be x ∈ R and X ≠± 1, f (x) be even function, G (x) be odd function, and f (x) + G (x) = 1 (x-1), find the solution of F () sum Find the analytic expressions of F (x) and G (x)
- 19. It is known that the function f (x) is an even function defined on the interval [- 2,2]. When x ∈ [0,2], f (x) is a decreasing function. If the inequality f (1-m) < f (m) holds, then the value range of real number m is () A. [−1，1 2) B. [1，2] C. [0，1 2） D. （−1，1 2）
- 20. It is known that even function f (x) defined on R satisfies f (x + 1) = f (1-x). It is proved that f (x) is a periodic function