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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
If f (x) = 2Sin (2x - π / 3) H (x) = 2Sin (2x + 2T - π / 3) the image is symmetric about (- π / 6,0), that is, the intersection point H (- π / 6) = 2Sin (2x-2 π / 3)
Given the function f (x) = cos2x / sin (x + π / 4), find the definition domain of function f (x) and find the value of sin2x if f (x) = 4 / 3
Definition domain: sin (x + π / 4) ≠ 0, then x ≠ K π - π / 4 (k is an integer from - ∞ to ∞)
f(x)=cos2x/sin(x+π/4)=4/3
3cos2x=4sin(x+π/4)
3(cos²x-sin²x)=4(sinxcosπ/4+cosxsinπ/4)
3(cos²x-sin²x)=2√2（sinx+cosx）
3(cosx+sinx)(cosx-sinx)=2√2(sinx+cosx)
cosx-sinx=2√2/3
(cosx-sinx)²=8/9
1-2sinxcosx=8/9
2sinxcosx=1/9
sin2x=1/9
It is known that the function f (x) = 2 times the root 3 cos squared (4 Molecular pai-x) + cos2x + 2A radical 3, X belongs to [0,2 molecule Given that the function f (x) = 2 times the root sign 3cos square (4-molecular-x) + cos2x + 2a-radical 3, the maximum value of X belonging to [0,2-numerator] is 6. (1) find the value of real number a (2) Find the monotone increasing interval of F (x)
f(x)=2√3[cos(π/4-x)]^2+cos2x+2a-√3
=√3cos(π/2-2x)+cos2x+2a
=√3sin2x+cos2x+2a
=2sin(2x+π/6)+2a
(1)0
Given the function f (x) = 1 / 4 (sin2x cos2x + radical 3) - radical 3 / 2sin2 (x - π / 4), X belongs to R. find the monotone increasing interval of F (x) Let the opposite sides of angles a, B, C in triangle ABC be a, B, C, and f (b) = 1 / 2, B = 2, find the maximum area of triangle ABC
I wonder if this will help
Given (1 + TaNx) / (1-tanx) = 3 + radical 2, find the value of cos? X + sinxcosx + 2Sin? X
∵ (1 + TaNx) / (1-tanx) = 3 + root two
∴ 1+tanx=3+√2-（3+√2)tanx
∴ (4+√2)tanx=2+√2
∴ tanx=(2+√2)/(4+√2)=(3+√2)/7
∴ cos²x+sinxcosx+2sin²x
= （ cos²x+sinxcosx+2sin²x）/(sin²x+cos²x)
Divide the numerator and denominator by cos? X at the same time
= (1+tanx+2tan²x)/(tan²x+1)
Substitute TaNx = (3 + √ 2) / 7
I think your question is wrong
Then we know that the root of cos2xf is 2?
cos2x=(1-tan²x)/(1+tan²x)
So f (x) = (1-x 2) / (1 + x 2)
f(-√2/2)=(1-1/2)/(1+1/2)
=1/3
If f (TaNx) = cos2x, then f (TaNx) = cos2x, then f (- radical 2 divided by 2) =?
F (TaNx) = cos2x = cos? X-sin? 2x = (COS? X-sin? X) / 1 = (COS? X-sin? X) / (sin? X + cos? X) = (1-tan? X) / (1 + tan? X) let t = TaNx, then: F (t) = (1-T?) / (1 + T? 2) so, f (- √ 2 / 2) = [1 - (1 /...)
Given the function y = asin (ω x + φ), in the same period, when x = π When x = 7 π If y = - 2, then the analytic formula of the function is () A. y=1 2sin（x+π 3） B. y=2sin（2x+π 3） C. y=2sin（x 2-π 6） D. y=2sin（2x+π 6）
The function y = asin (ω x + φ), in the same period, when x = π
When x = 7 π
At 12, the minimum value y = - 2 is obtained,
So a = 2,
ωπ
12+Φ=π
2，ω7π
12+Φ=3π
Two
The solution is: ω = 2
φ=π
Three
The analytic formula of the function is y = 2Sin (2x + π)
3）
Therefore, B is selected
As shown in the figure, fold the rectangular paper ABCD, first fold out the crease BD, and then fold the ad edge to coincide with the diagonal BD to get the crease DG. If AB = 2, BC = 1, find the length of Ag.
T = 2 (π)
3-0）=2π
Three
∴ω=2π
T=3，
According to the maximum and minimum values, a = 2 − (− 2)
2=2
Substituting x = 0 into the analytic formula, we get 2Sin, φ = - 2, and φ = - π
Two
Therefore, the analytic expression of the function is y = 2Sin (3x - π)
2）
So the answer is: y = 2Sin (3x − π)
2)．
Y = asin (Wx + φ), in the same period, when x = π / 12, the maximum value of Y is 2, and when x = 7 / 12 π, the minimum value of Y is - 2 Among them, a > 0, w > 0, 0
∵A>0
∴A=[2-(-2)]/2=2
Period T = 2 × (7 π / 12 - π / 12)
= Pi
And W > 0
∴w=2π/T=2
∴y=2sin(2x+φ)
When x = π / 12, y = 2
That is, 2Sin (π / 6 + φ) = 2
∴sin(π/6+φ)=1
∵0
RELATED INFORMATIONS
- 1. The known function y = asin (ω x + φ), |φ|
- 2. 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
- 3. 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?
- 4. How to learn the properties of the function y = asin (Wx + φ)? It feels so difficult
- 5. Compulsory exercise 1.2b group 1~
- 6. 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!
- 7. Find the area of the plane figure surrounded by the curve y = x and y = X
- 8. 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 ()
- 9. If cosx + cosy = 1 / 2, SiNx siny = 1 / 3, then cos (x + y) =?
- 10. Find the value range and minimum positive period of the function f (x) = 2cos (x + PIA / 4) cos (x-pia / 4) + root sign 3sin2x
- 11. 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?
- 12. Reduction function f (x) = cos2x / sin (45 '- x)
- 13. It is proved that: (1 + cot? α) / (1-cot? α) = 1 / (2Sin? α - 1) urgent!
- 14. F (x) is an even function defined on R when x
- 15. 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
- 16. 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
- 17. 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]
- 18. 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)=______ .
- 19. F (x) = (1 + cos2x) sin ^ 3x to find out whether the minimum positive period of a function is odd or even,
- 20. 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)