In the plane rectangular coordinate system xoy, there is a point P (P is in the second quadrant), Op = 8. If the angle between OP and the positive half axis of X axis is 145 °, then the coordinate of point P is

In the plane rectangular coordinate system xoy, there is a point P (P is in the second quadrant), Op = 8. If the angle between OP and the positive half axis of X axis is 145 °, then the coordinate of point P is

Let P (x, y) (x0)
Because OP = 8, the angle between OP and the positive half axis of X axis is 145 degrees
So x = - 8 * cos (45 °) = - 4 √ 2
y=8*sin(45°)=4√2
So the coordinates of point P are (- 4 √ 2,4 √ 2)

In the plane rectangular coordinate system xoy, two points a and B are respectively on the positive half axis of x-axis and y-axis, and OA = ob = 2,
And s △ ABC = 4, find the coordinates of point D

AB midpoint coordinates (1,1)
Triangle height = 2x4 / double root 2 = double root 2
So point d coordinates (1 + double root 2, 1 + double root 2)

As shown in the figure, in the plane rectangular coordinate system, point E is in the first quadrant, point F is on the positive half axis of X axis, OE = 2 √ 2,

(1) ∵ the line of CD is perpendicular to the X axis
∵∠CAD=(1/2)∠BAD=45°;∠EOF=45°.
Therefore, CD is perpendicular to X axis
If eg is perpendicular to the x-axis at g, ∠ EOF = 45 °, then eg = og = (√ 2 / 2) OE = 2, that is, point E is (2,2)
If Tan ∠ EFO = eg / FG = 1 / 2, then FG = 2, eg = 4, of = 6
(2) When point C and e coincide, the moving distance of point C is: 2 √ 2-ac / 2 = 2 √ 2 - √ 2 / 2 = (3 / 2) √ 2
So the value of T is: (3 / 2) √ 2 △ 2 = 3 / 2 (seconds)
(3) When 0 seconds ≤ t ≤ 1 / 2 seconds: S = (1 / 2) T & # 178; + (1 / 2) t + 1 / 8;
When 1 / 2 second