20,000,000 + 6,000,000 + 100,000 + 40,000 + 3,000 + 60 + 2
Answer: sqrt(2)/2 which is choice D
======================================================
Explanation
(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).
The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle
180-135 = 45
Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2
sine is positive in quadrant 2
------------
Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2
Recall that y = sin(theta).
Ignore the fact that it says limit because when sin (pi) is here it is not an Undefined Point, whatever value the calculator says is sin(pi) is the answer.
A rotation 270° counterclockwise about the origin is the same as rotation 90° clockwise about the origin and has a rule:
(x,y)→(y,-x).
Then:
- D(−2,4)→D'(4,2)
- E(4,7)→E'(7,-4)
- F(10,3)→F'(3,-10)
- G(8,0)→G'(0,-8)
Answer: the coordinates of vertices of quadrilateral D′E′F′G′ are D'(4,2), E'(7,-4), F'(3,-10), G'(0,-8).