![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
If f (x) = Tan (Wx + π / 3) (W > 0), the length of the line segment of two adjacent sectional lines y = π / 4 is π / 4 (1) The analytic formula of ball f (x) and the value of F (π / 4) (2) Find the monotone interval of F (x)
1、
There is a period difference between two adjacent branches
So t = π / 4
So π / w = π / 4
w=4
So f (x) = Tan (4x + π / 3)
f(π/4)=tan(π+π/3)
=tan(π/3)
=√3
2、
TaNx is an increasing function in a period
Then K π - π / 2
The function f (x) = Tan ω x (ω ＞ 0) has two adjacent tangent lines y = π 4. If the length of the line is π 4, then the value of F (π 4) is ()
A. 0B. 1C. -1D. π4
The length of the line segment obtained from the two adjacent tangent lines y = π 4 of the function image is π 4. The period of the function f (x) is π 4. From π ω = π 4, we get ω = 4. So we choose a
If the function f (x) = tanwx (W > 0), the length of the line segment is 6 π
Finding f (π / 2)
You know, tangent function image is a continuous translation
Period = π / w = 6 π
w=1/6
F (π / 2) = Tan π / 12 = 2-radical 3
Application of discriminant for roots of quadratic equation with one variable
Let a, B and C be the lengths of the three sides of △ ABC, and try to judge the roots of the quadratic equation A & sup2; X & sup2; + (B & sup2; + A & sup2; - C & sup2;) x + B & sup2
Discriminant = (b ^ 2 + A ^ 2-C ^ 2) ^ 2-4a ^ 2B ^ 2
=(b^2+a^2-c^2+2ab)(b^2+a^2-c^2-2ab)
=[(a+b)^2-c^2][(a-b)^2-c^2]
=(a+b+c)(a+b-c)(a-b+c)(a-b-c)
The side length of triangle is greater than 0
So a + B + C > 0
The sum of the two sides of a triangle is greater than the third side
So a + B-C > 0
a-b+c>0
a-b-c=a-(b+c)
What are real numbers and imaginary numbers?
I just want to know in advance!
Plural
Complex number: is the general name of real number and imaginary number. The basic form of complex number is a + bi, where a and B are real numbers, a is real part, Bi is imaginary part, I is imaginary unit. On the complex plane, a + bi is point Z (a, b). Real number: the general name of complex number, rational number and irrational number without imaginary part
Given that one root of the quadratic equation XX + MX + n = 0 with real coefficients is 1-3i, find the value of M + n
One root is 1 -- 3I, and the other root must be 1 + 3I,
So m = -- [(1 + 3I) + (1 -- 3I)] = -- 2,
n=(1+3i)(1--3i)=10,
So m + n = 8
The two roots of a quadratic equation with coefficient 1 are 2 and 3 respectively
How much can you write when the coefficient of quadratic term is not unique?
Y=(x-2)(x-3)
When the coefficient of quadratic term is not unique, we can write innumerable
Y=a(x-2)(x-3)
Three analytic geometry problems about circle,
1. Let a be the moving point on the circle (X-2) ^ 2 + (Y-2) ^ 2 = 1, then the maximum distance from a to the line x-y-5 = 0 is?
2. The equation of the circle passing through the intersection of the circle x ^ 2 + y ^ 2-x + Y-2 and x ^ 2 + y ^ 2 = 5 with the center of the circle on the straight line 3x + 4Y = 1 is?
3. Given that a circle passes through two intersections of (line 2x + y + 4 = 0 and circle C: x ^ 2 + y ^ 2 + 2x-4y + 1 = 0) and has the smallest area, the equation of the circle is?
I will answer a question. Help!
1+5√2/2
(x+1)^2+(y-1)^2=25/2
(x+13/5)^2+(y-6/5)^2=4/5
Given that a (- 2,0), B (2,0), and point P move on the circle (x-3) &# 178; + (y-4) &# 178; = 4, then the minimum value of | PA | &# 178; + | Pb | &# 178; is obtained
Let P (3 + 2 cosa, 4 + 2 Sina), then PA ^ 2 = (5 + 2 COSA) ^ 2 + (4 + 2 Sina) ^ 2 = 25 + 20 cosa + 4 (COSA) ^ 2 + 16 + 16 Sina + 4 (Sina) ^ 2 = 20 cosa + 16 Sina + 45, Pb ^ 2 = (1 + 2 COSA) ^ 2 + (4 + 2 Sina) ^ 2 = 4 cosa + 16 Sina + 21, PA ^ 2 + Pb ^ 2 = 24 COA + 32 Sina + 66 = 40 sin [a + arctan (3 / 4
Simple, don't tell me to use the formula of distance from point to line
The straight line y = KX + B, the slope is k, and the known point is a (a, b)
Let the symmetric point be p (x, y), then the coordinates of the midpoint of AP are x '= (x + a) / 2, y' = (y + b), which must be on y = KX + B, and then a equation (1) is obtained
If AP is perpendicular to y = KX + B, then the slope of AP = - 1 / K, that is, (y-b) / (x-a) = - 1 / K, (2)
(1) (2) get the P coordinate
RELATED INFORMATIONS
- 1. If the length of the segment is π / 4, then the value of F (π / 3) is? A.√3/3 B.-√3/3 C.√3 D.-√3
- 2. If y = tanwx (W > 0), y = (Π / 4), then y = (Π / 4)=
- 3. Who knows how to find the area of ellipse? Area formula
- 4. When we get to the area formula of a circle When we deduce the area formula of a circle, we divide the circle into several equal parts to form an approximate rectangle. It is known that the area of a circle can be calculated when the length of the rectangle is 6.42 cm more than the width
- 5. Definite integral of high school mathematics .3 ∫ - 1 how to find the original derivative of 2x ^ 5 in 2x ^ 5DX? What are the good steps What kind of thinking should be used to think about how to find this problem first and then how to deal with it
- 6. It is known that f (x) is a quadratic function, f (- 1) = 2, f ′ (0) = 0, ∫ 01F (x) DX = - 2. (1) find the analytic expression of F (x); (2) find the maximum and minimum of F (x) on [- 1,1]
- 7. A problem of definite integral calculation, The questions are as follows: ∫ (1-cosx) & sup2; multiply by 1-cosx DX under quadratic root It didn't work out, PS: Please list the trigonometric function formulas to be used, and make clear what is set to t by substitution, The value range of X is 0 -- 2 π
- 8. A very simple definite integral problem Find the volume of the body of revolution of the semi ellipse X & sup2 / 9 + Y & sup2 / 4 = 1 (Y > = 0) rotating around the x-axis
- 9. A problem of area and tangent by definite integral Find a tangent line of the curve y = LNX in the interval (2,6), so that the area of the figure enclosed by the tangent line and x = 2, x = 6, and the curve y = LNX is the smallest
- 10. ∫ (upper limit 1, lower limit-1) (2-x ^ 2) ^ (3 / 2) DX
- 11. The concepts of monotonicity and parity of functions
- 12. How to find the integral of the fourth power of Sint multiplied by the square of cost?
- 13. How to calculate the area of irregular figure
- 14. If the area of the triangle formed by the line y = 2x + B and the two coordinate axes is 7, then B= The square of 3 (X-Y) is multiplied by the cube of [minus two thirds (Y-X)] and written in the form of the nth power of K (X-Y) A. The fifth power of minus 2 (X-Y) B. the sixth power of minus 2 (X-Y) C. The fifth power of minus 2 (X-Y) d. The sixth power of minus 2 (X-Y)
- 15. Should the radius of curvature of a cardioid be transformed into a parametric equation in Cartesian coordinates, or can we just directly find the derivative of R with respect to θ?
- 16. How can the polar equation P = 2 be transformed into a rectangular equation? I know it's a circle, but I need standard transformation steps
- 17. High polar coordinates used to calculate double integral, do not understand the meaning, please guide
- 18. The transformation of polar coordinates into rectangular coordinates by double integration 1. Let x = RCOs θ y = rsin θ, why is the corresponding rectangular coordinate equation of R = 2cos θ (x-1) ^ 2 + y ^ 2 = 1 2. 2cosθ< r < 2 0
- 19. Asking for help with the proof of freshman If f (x) is continuous on the interval [a, b], and f (a) < A, f (b) > b, then there is f (ξ) = 0 on ξ ∈ (a, b)
- 20. As shown in the figure, the curve C is the image of the function y = 6 / X in the first quadrant, and the parabola is the image of the function y = - x ^ 2-2x + 4, The point PN (x, y) (n = 1,2,3 ··) is on the curve C, and X and y are integers. (1) find out all the points PN (x, y); (2) take any two points in PN as a straight line, and find out the number of all different lines. (3) take any straight line from (2), and find out the probability that the straight line and parabola have a common point