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If for any real number a, f (Sina + COSA) = sinacosa, find f (0) + F (1)?
Let x = Sina + cosa
x²=sin²a+cos²a+2sinacosa
=1+2sinacosa
sinacosa=(x²-1)/2
f(x)=(x²-1)/2
f(0)+f(1)=-1/2+0=-1/2
In the polar coordinate system, the distance between the point m (√ 5, arctan2) and the straight line ρ (COS θ + sin θ) = 1 is 0
In the rectangular coordinate system, if the coordinate of m point is (1,2) and the linear equation is x + y = 1, then the distance between M and the straight line is √ 2
In polar coordinates, the maximum distance between the point on the circle ρ = 2cos (θ + π / 4) and the point on the straight line ρ sin (θ + π / 4) = √ 2 is -?
Circle ρ = 2cos (θ + π / 4)
ρ=√2cosθ-√2sinθ
x^2+y^2=√2x-√2y
(x-√2/2)^2+(y+√2/2)^2=1
Center (√ 2 / 2, - √ 2 / 2), radius r = 1
Straight line ρ sin (θ + π / 4) = √ 2
x+y=2
The distance from the center of the circle (√ 2 / 2, - √ 2 / 2) to x + y = 2
d=√2
The maximum distance is: 1 + √ 2
In polar coordinates, the distance from point (3, π 2) to line ρ sin (θ - π 4) = 22 is___ ．
The point P (3, π 2) is transformed into P (0, 3). The straight line ρ sin (θ - π 4) = 22 is expanded into 22 (ρ sin θ - ρ cos θ) = 22, which is transformed into X-Y = 4, and the distance from point P to the straight line d = | 0-3-4| 2 = 722, so the answer is: 722
RELATED INFORMATIONS
- 1. In polar coordinate system, the equation of line L is ρ sin θ = 3, then the distance from point (2, π 6) to line L is () A. 4B. 3C. 2D. 1
- 2. If P (Sina, COSA) is a point on the terminal edge of angle a, what is the value of a
- 3. It is known that f (x) = log2 (xcosa + Sina), a belongs to (π / 2,3 π / 4) 1.f（cosA/[1+sinA])=0 2. When x belongs to [- 1,1], f (x) is always greater than or equal to - 1, and the value range of sin (a + [π / 4]) can be obtained 3) If f (1-4sina)
- 4. The common equation of C is xsina ycosa Sina = 0, which makes a vertical line of C through the origin. Why is the vertical foot (Sina ^ 2, - cosasina)
- 5. On the number axis, the distance from the point of √ 7 to the origin is equal to________ . Chapter 2 real numbers I'm going to use it tonight,
- 6. The corresponding points of rational number ABC on the number axis are a, B and C, and their positions are shown in the figure below b
- 7. The following statements are correct: (1) 0 is the number with the smallest absolute value; (2) the number whose absolute value is equal to itself is a positive number; (3) the numbers on both sides of the origin on the number axis are opposite to each other; (4) the absolute value is larger but smaller when compared with the two numbers A. 1 B. 2 C. 3 d. 4
- 8. The positions of a, B and C on the number axis are shown in the figure below, which is simplified as follows: 1. |a + B | + |b-c | - A + C | 2. |2a-b | + |a-3c | - B + 3C| ———————|———|—|————|———————→ c a 0 b
- 9. It is known that: as shown in the figure, the real numbers corresponding to points a, B, C and D are all integers. If point a corresponds to real number a, point B corresponds to real number B, and b-2a = 7, then the origin on the number axis should be______ Point
- 10. What is the ten digit number of 1 + 11 + 111 + 1111. + 11.11 (thirty ones) = s
- 11. The range of y = Sina / (COSA + 2)
- 12. The vertex o (0,0), a (2,1), B (10,1) of triangle OBC, the line CD is perpendicular to the X axis and bisects the area of triangle ABC. If D (x, 0), then the value of X is
- 13. It is known that the polar coordinates of the two ends of the line segment passing through the pole are P1 (ρ 1, θ 1) P (ρ 2, θ 2 + π), and the midpoint m of p1p2 is proved（ It is known that the polar coordinates of the two ends of the line segment passing through the pole are P1 (ρ 1, θ 1) P (ρ 2, θ 2 + π). It is proved that the midpoint of p1p2 is m (ρ 1 - ρ 2, θ 1)
- 14. In the triangle AOB, the coordinates of two points AB are (- 4, - 6), (- 6, - 3) respectively, and the area of the triangle can be calculated (hint: the area of the triangle AOB can be seen from
- 15. As shown in the figure, in the triangle AOB, the coordinates of a and B are (- 4, - 6), (- 6, - 3), respectively. Calculate the area of the triangle AOB (hint: the area of the triangle AOB can be regarded as the area of a trapezoid minus the area of some small triangles)
- 16. In the polar coordinate system, we know two points a (6, π / 6) B (6, 2 π / 3) to find the polar coordinates of the midpoint of ab,
- 17. Solving the right focus polar coordinate equation of mathematical conic Is it the same
- 18. Given the quadratic function f (x), the vertex of the image is (- 1,2), and through the origin, find f (x)
- 19. If we know that the vertex of angle a coincides with the origin, the starting edge coincides with the positive half axis of X axis, and the ending edge is on the line y = 3x, ask cos2a =?
- 20. If P (4, y) is a point on the edge of angle A and Sina = - 2 times the root 5 / 5, then y =? 7