![](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>)
In the polar coordinate system, find the polar coordinate equation of a line or circle which is suitable for the following conditions: (1) a line passing through the pole with an inclination angle of π / 3 (2) A line passing through a point (2, π / 3) and perpendicular to the polar axis (3) A circle whose center is a (1, π / 4) and radius is 1 (4) A circle whose center is (a, π / 2) and radius is a
1. θ = π / 3 or θ = 4 π / 3
2、ρcosθ=1
3、ρ=2cos（θ-π/4）
4、ρ=2asinθ
I love you... This angle symbol is too hard to type... If you can't, you can write out the representation of the rectangular coordinate system first, and then replace it with L ^ 2 = x ^ 2 + y ^ 2. L is the length, and that letter is hard to type...
In the polar coordinate system, find the polar coordinate equation of the line or circle which is suitable for the following conditions: through the pole, the straight line whose inclination angle is π / 3
If the inclination angle is π / 3, the straight line is θ = π / 3
The "polar coordinate" equation of the circle with the center at a (1, π / 2) and radius 1,
Transformation formula between polar coordinate equation and rectangular coordinate equation
x=r*cosθ
y=r*sinθ
The above equation is very easy,
(x-1)^2+(y-π/2)^2=1
Take the upper transformation formula into the rectangular coordinate equation of the circle and simplify it again, isn't it?
It is known that {an} is an arithmetic sequence whose first term is a and tolerance is 1, BN = 1 + Anan. If BN ≥ B8 holds for any n ∈ n *, then the value range of a is______ .
The general formula of {an} sequence is an = a + n-1, ∵ BN = 1 + Anan = 1 + 1An = 1 + 1A + n − 1. ∵ BN ≥ B8 ∵ 1 + 1An ≥ 1 + 1a8, that is, 1An ≥ 1a8. The sequence {an} is an increasing sequence, and the tolerance is 1, ∵ A8 = a + 8-1 < 0, A9 = a + 9-1 > 0
The general form of transforming equation (x + 2) ^ 2 = (3x-4) ^ 2 into quadratic equation with one variable is___ Where the coefficient of quadratic term is___ The coefficient of the first term is___ %
The coefficient of the first term is______ The constant term is_____
The general form of the equation (x + 2) ^ 2 = (3x-4) ^ 2 is 8x ^ 2-28x + 12, in which the coefficient of quadratic term is 8 and the coefficient of primary term is 2800%
If 0 ＜ a ＜ 1 is known, then the number of real roots of the equation a ^ | x | = | log a x | is?
To find the number of real roots of the equation is to find the number of intersections of the images of two corresponding functions
The real root of the equation a ^| x | = | log a x | can be transformed into the intersection of the images of y = a ^| x |, y = | log a x |
Y = a ^ | x | is an even function. Draw the image of y = a ^ x (x > 0) and fold it along the y-axis to get the image of y = a ^ | x |
The function value of y = | log a x | is positive. First, draw the image of y = log a x, fold up the part below the X axis, and get the image of y = | log a x |
It is found that there are two intersections, so the corresponding equation has two real roots
If the function f (x) = cos2x + SiNx cosx TX increases monotonically on [0, π / 2], then the value range of real number T is?
The answer is (negative infinity, root 2-2]
Derivation
The first term of the arithmetic sequence {an} is a, the tolerance is D; the first term of the arithmetic sequence {BN} is B, the tolerance is e, if CN = an + BN, (n is greater than or equal to 1) and C1 = 4, C2 = 8. Find the general term formula of the sequence (CN)
Can we use C2 minus C1 to calculate the tolerance, and then directly say that the formula is CN equals 4 minus (n minus 1) 4 equals 4N? If not, please tell me why?
sure,
an=a+(n-1)*d
bn=b+(n-1)*e
cn=(a+b)+(n-1)*(d+e)
A + B is the first term and D + e is the tolerance
If x = 4 is a root of the quadratic equation x2-3x = A2, then the value of constant a is___ .
Substituting x = 4 into the equation x2-3x = A2, we can get 16-12 = A2, and the solution is a = ± 2, so the answer is: a = ± 2
If the equation (A-1) &# 178; - 2x + 1 = 0 has real roots, then the value range of a is
A = 1, then the equation is - 2x + 1 = 0
There are real roots
a≠1
It's a quadratic equation of one variable
So the discriminant △ = 4-4 (A-1) > = 0
A
This is a linear equation of one variable. No matter what value a takes, X has real roots
RELATED INFORMATIONS
- 1. Polar coordinate equation of circle with center C (2, π) and radius 2
- 2. In polar coordinates, the equation of a circle with (A2, π 2) as its center and A2 as its radius is______ .
- 3. In polar coordinate system, given that the center of circle C is C (1, π 4) and the radius is 1, the polar coordinate equation of circle C is___ .
- 4. Find the polar coordinate equation of the circle whose center is (- 3, π / 4) and passes through the pole o
- 5. The range of F (x) = (1 + Sina) (1 + COSA) (a is a real number)
- 6. If the corresponding points of two rational numbers on the number axis are on both sides of the origin, then the quotient of the two numbers A is a positive number, B is a negative number C is zero, D can be positive or negative
- 7. Given the position of rational numbers a and B on the number axis as shown in the figure (the absolute value of a is greater than B), then | A-B | is equal to A.A + B B. - (a + b) c.a-b d.b-a a0,———⊥——————————⊥—⊥————————→ a 0 b
- 8. On the number axis, the point representing the negative number is at () of the origin, the point representing the positive number is at () of the origin, and the number represented by the origin is () On the number axis, the distance from point a of 205 to the origin is (), the distance from point B of - 2.5 to the origin is (), and the distance between two points is () From the above question, we can guess that there are () points on the number axis with a distance of 4.5 from the origin, and the points that meet the conditions represent () A point starts from the origin of the number axis, first moves 2 units of length to the left, and then moves 3 units of length to the right. The number represented by the point is () Judgment: each store on the number axis represents a rational number The distance from the number axis to the origin is equal to 2 points of unit length, which means the number is 2 Given that there is a line segment of 100 unit length on the number axis, how many points representing integers may be covered by the changed line segment? The 205 of the first question is 2
- 9. The corresponding points of rational numbers a, B and C on the number axis are shown in Figure 2, where o is the origin. B > O > C > A Simplify | A-B | + | a + B | + | B-C | - | a|
- 10. On the number axis, point a (representing integer a) is on the left side of origin o, and point B (representing integer b) is on the right side of origin O. if A-B = 2013 and AO = 2BO, then the value of a + B is () A. -1242B. 1242C. 671D. -671
- 11. It is known that the vertex of angle α is at the origin, and the starting edge is the positive half axis of X axis. If the end edge of angle α passes through the point P (√ 3, y), and sin α = - √ 2 △ 4, y ≠ 0 (1), judge the quadrant where angle α is located (2), and calculate the values of cos α and Tan α
- 12. The vertex of the known angle α coincides with the origin of the rectangular coordinate system, the starting edge is on the positive half axis of the x-axis, and the final edge passes through the point P (- 1,2). The values of sin α and COS (π + α) are calculated
- 13. The vertex of the known angle α coincides with the origin of the rectangular coordinate system, and the starting edge is on the non negative half axis of the X axis It is known that the vertex of the angle a coincides with the origin of the plane rectangular coordinate system, the starting edge is on the non negative half axis of the X axis, and the final edge passes through the point P (- 1,2)
- 14. In the space rectangular coordinate system o-xyz, the distance between the point P on the coordinate axis and a (1,1,1) is equal to the root sign 3, so the point P has the same number
- 15. If the distance from the intersection point of the line y = 3x + B and Y axis to the origin is 3, then the function expression of the line is
- 16. Let a be an acute angle, if Sina =? Then a =? If Tan a = root 3 / 3, then a =?
- 17. Sina / 2 = 4 / 5, cosa / 2 = - 3 / 5, which quadrant is a
- 18. What is the formula of auxiliary angle
- 19. Find the maximum and minimum of the following functions. (1) y = Sina - root 3cosa, a belongs to R (2) y = Sina + cosa, a belongs to R
- 20. Given the function y = Tan + cosa / Sina, a belongs to (0, π / 2), find the minimum value of Y y=tana+cosa/sina,