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Simplify e ^ in (1 / 2) function
e^In(1/2)=1/2
Simplification of mathematical functions 2cos10°-sin20°/cos20°=? sin40°+2cos70°/sin50°=?
It's OK to change cos10 into cos (30-20). The root is 3
Change cos70 into sin20, sin20 into sin (60-40) is OK, root 3
According to the following conditions: (what I want to know is whether it is easier to replace the problem directly or to simplify it first and then bring it in) f(x)=sin(x+π/4)+2sin(x-π/4)-4cos2x+3cos(x+3π/4) (1)x=π/4 (2)x=3π/4 If you simplify first, how should you simplify it?
General trigonometric function problem known angle to find the value of the function is first simplified and then replaced by simple, but this problem directly into the simple
On simplifying function in Senior High School Given Tana = radical 2 / 2, find the value of COS ^ 2 (Wu - a) + sin (Wu + a) * cos (Wu - a) + 2Sin ^ 2 (a - Wu)
[cos(π-a)]^2+sin(π+a)cos(π-a)+2[sin(a-π)]^2
=(-cosa)^2+(-sina)(-cosa)+2(-sina)^2
=(cosa)^2+sinacosa+2(sina)^2
=[(cosa)^2+sinacosa+2(sina)^2]/[(cosa)^2+(sina)^2]
=[1+tana+2(tana)^2]/[1+(tana)^2]
=(1 + radical 2 / 2 + 1] / [1 + 1 / 2] = (4 + Radix 2) / 3
Simple simplification questions! Is 6 + 2 radical 7 / 6 the simplest?
no
Original formula = 6 + 2 * (Radix 42 / 6)
=6 + (Radix 42 / 3)
This is the simplest
For example, how to simplify the function in question 1 1. (2011 · new curriculum standard nationwide) let the minimum positive period of the function f (x) = sin (ω x + φ) + cos (ω x + φ) be π, and f (- x) = f (x), then () A. F (x) decreases monotonically B. F (x) decreases monotonically C. F (x) increases monotonically D. F (x) increases monotonically 2. (investigation in Xi'an, 2013) Let f (x) be an odd function defined on R, and when x ≥ 0, f (x) monotonically decreases. If X1 + x2 > 0, then the value of F (x1) + F (x2) () A. Constant positive value B. equal to zero C. Constant negative D. cannot determine positive and negative Please write down the process,
One
f(x)＝sin(ωx＋φ)＋cos(ωx＋φ)
=√2[√2/2*sin(ωx＋φ)＋√2/2cos(ωx＋φ)]
=√2sin(wx+φ+π/4)
From 2 π / w = π, w = 2
∴f(x)=√2sn(2x+φ+π/4)
∵f(-x)=f(x)
/ / F (x) is an even function, and the image is symmetric about the y-axis
Then when x = 0, f (0) is the maximum
That is sin (φ + π / 4) = ± 1
∴φ+π/4=kπ+π/2,kπ∈Z
∴φ=kπ+π/4,k∈Z
When k = 0, take φ = π / 4
∴f(x)=√2sin(2x+π/2)=√2cos2x
As for the option, the condition input is not complete and cannot be judged
Two
Let f (x) be an odd function defined on R,
When x ≥ 0, f (x) decreases monotonically,
So x0
∴x1>-x2
∴f(x1)
The known function f (x) = cos2x / [sin (π / 4-x)]
cos2x=sin(π/2-2x)=2sin(π/4-x)cos(π/4-x)
cos2x/[sin(π/4-x)]
=2sin(π/4-x)cos(π/4-x)/[sin(π/4-x)]
=2cos(π/4-x)/
Given the function f (x) = (sin2x cos2x + 1) / (2sinx), find the domain of F (x) The known function f (x) = (sin2x cos2x + 1) / 2sinx (1) Find the definition domain of F (x) (2) Let α be an acute angle and Tan α = 4 / 3, then find the value of F (α)
1. SiNx ≠ 0, x ≠ K π. Tan α = 4 / 3, sin? α + cos? α = 1sin α / cos
The logic function f = AB + a'c + b'c is simplified by formula method,
The logic function f = AB + a'c + b'cf = AB + a'c + b'c = AB + a'c (B + B ') + b'c (a + a') = AB + a'bc + a'b'c + a b'c + a'b'c = AB + a'bc + a b'c + a'b'c = AB + (a'B + ab ') C + a'b'c = AB + C + a'b'c = AB + C + a'b'c = AB + C
The following logic functions are simplified by formula method
F = AB'+BD+CDE+A'D
= AB'+(A'+B)D+CDE
= (A'+B)'+(A'+B)D+CDE
=(A'+B)'+D+CDE
=(A'+B)'+D(1+CE)
= (A'+B)'+D
=AB'+D
RELATED INFORMATIONS
- 1. How to use formula theorem to simplify the following logic functions in digital circuit? 1.F=A/ B + A/ C + B/C/ + A/D A/+B/C/+D】 =How to get + A / C / A / C / b =A/B+B/C/+A/+D =A/+B/C/+D 2.F= A/B/ + A/C/D + AC + BC/ A/B/ + BC/ + AC】 3.F= A(B+C/) + A/ (B/+C) + B/C/D + BCD AB + A/C + AC/ + A/B】 Requirements: use the formula theorem of logic function to simplify the above three formulas, write the solution process (if possible, it's better to be more detailed), can't use Karnaugh map to simplify My process of simplification (all wrong) 1.F= A/B +A/C + B/C/+AD =A/BC+A/BC/+A/BC+A/B/C+AB/C/+A/B/C/+AD =A/BC+A/BC/+A/B/+AB/C/+AD =A/+AB/C/D/+AD A/+B/C/+D】 3.F= A(B+C/) + A/(B/+C) + B/C/D + BCD =AB+AB/C/ + A/B/+A/BC + AB/C/D + A/B/C/D + ABCD + A/BCD =AB+AB/C/+ A/B/+ A/BC AB + A/C + AC/ + A/B】
- 2. Let f (x) be a function on R and satisfy f (0) = 1, and for any real number x, y has f (X-Y) = f (x) - Y (2x-y + 1), and find the expression of F (x)
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- 4. It is known that the function y = asin (ω x + φ) has a maximum value of 2 when x = π - 3 and a minimum value of - 2 when x = 0 in the same period
- 5. A series of corresponding values of the known function f (x) = asin (Wx + φ) + B (a > 0; W > 0) are as follows: For detailed explanation,
- 6. The image of the function y = asin (Wx + FAI) W
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- 8. The function y = asin (Wx + ψ) + B (W 〉 0, |ψ||Π / 2) has the highest point (Π / 12,3) and the lowest point (7 Π / 12, - 5) in the same period Analytic formula of
- 9. Draw the function image of y = - 3x square, y = one third of x square; draw the function image of y = 4x square; y = - quarter x square
- 10. ·What is the area of the closed plane figure enclosed by the curve y = x ^ 2, the straight line y = 2x-1 and the X axis?
- 11. . given cot α = 3, find the value of cos? α + 1 / 2sin2 α? (to calculate the process) 2sin2 α is the denominator
- 12. Given that SiNx = asin (x + β), Tan (x + β) = sin β / (COS β - a)
- 13. Let f (x) be an even function defined on R. when x > 0, f (x) + XF '(x) > 0, and f (1) = 0, then the solution set of inequality XF (x) > 0 is () A. （-1，0）∪（1，+∞） B. （-1，0）∪（0，1） C. （-∞，-1）∪（1，+∞） D. （-∞，-1）∪（0，1）
- 14. It is known that f (x) is an even function defined on R, and an odd function g (x) defined on R passes through the point (- 1,1) If G (x) = f (x-1), then f (2007) + F (2008) =?
- 15. It is known that the function f (x) is an even function defined on R, and when x ≤ 0, f (x) = - x2 + X. The expression of F (x) and the analytic expression of F (x) when x > 0 are obtained
- 16. Let f (x) be an even function defined on R and increase monotonically in the interval (- ∞, 0), f (2a ^ 2 + A + 1)
- 17. Let a > 0, f (x) = [(x of E) / a] + [A / (x of E)] be even functions on R (1) find the value of A (2) prove the increasing function of F (x) on (0, + ∞)
- 18. It is known that f (x) = asin (ω x + π / 4) (where x ∈ R, a > 0, ω > 0) has a maximum value of 2 and a minimum period of 8 (1) Find the analytic formula of function f (x) (2) if the abscissa of two points P and Q on the image of function f (x) are 2,4,0, then find the value of cos ∠ p0q
- 19. The necessary and sufficient condition for the quadratic function y = ax ^ 2 + BX + C to be even function is proved
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