SOLUTION: The calculator screen shows a regular pentagram whose vertices lie on a unit circle with centre (0,0). The values on the screen refer to the vertex marked with the cursor…bottom le
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Question 1014245: The calculator screen shows a regular pentagram whose vertices lie on a unit circle with centre (0,0). The values on the screen refer to the vertex marked with the cursor…bottom left vertex. The values indicate the coordinates of the corresponding angle in standard position. (This was the fourth point plotted. With each new point plotted a straight line joins to the previous point.)
a) Write the angle in standard position, in degrees corresponding to each vertex.
b) Write the coordinates of each vertex.
(Shows a pentagram picture on a graphing calculator, in the bottom left says x=-.588, y=-.809 and a dot on the leftmost bottom triangle vertex) Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! I assume your calculator screen shows a regular pentagon, looking like this: Point , with ,
is at a distance from the origin,
so its x- and y-coordinates are cosine and sine of the corresponding angle in standard position.
The same goes for all the other vertices of the pentagon. --> .
That tangent corresponds to angles of in the first quadrant (with positive sign and cosine), and in the third quadrant (with negative sign and cosine).
That is the measure of the angle in standard position corresponding to vertex A.
In a regular pentagon, the central angles (such as AOB) measure ,
so once we know the angle for one vertex,
we find the angle for adjacent vertices by adding or subtracting .
For vertex B;
For E:
For D:
For C:
