barrons question on polar curve

Archive SAT Subject Test Preparation
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<p><a href=“http://s23.postimg.org/6xjv0gtbf/Capture.png[/url]”>http://s23.postimg.org/6xjv0gtbf/Capture.png&lt;/a&gt;&lt;/p&gt;

<p>I understood the explanation given here </p>

<p><a href=“http://s21.postimg.org/m3bo2cg3r/Capture.png[/url]”>http://s21.postimg.org/m3bo2cg3r/Capture.png&lt;/a&gt;
but I dont understand how they got the fact that the length of x and of y was 1?
if x+y=1 shouldnt it be x=.5 and y=.5?</p>

2

<p>i first graphed r=1/sin () + cos ()
from the graph i could see that it formed a right angled triangle wid the x and y axes.
now, i had to figure out the base and height
length of the base can be found be using the trace function. i put theta=0 and i got r=1. that’s my base.
next, i put in theta= pi/2 and i got r=1. which is the height.
then using 1/2 * base * height, i got area = 0.5</p>

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<p>Um what if I dont have a graphing calculator?</p>

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<p>and another question</p>

<p><a href=“http://s14.postimg.org/5klv6hf41/Capture.png[/url]”>http://s14.postimg.org/5klv6hf41/Capture.png&lt;/a&gt;&lt;/p&gt;

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<p>What’s the answer for the last question ?</p>

6

<p>B I finally solved it I am stuck on the previous question though I dont have a calculator</p>

7

<p>1/(sin+cos)=r
rsin+rcos=1
rsin=x
rcos=y</p>

<p>So, rsin+rcos=1=x+y
x+y=1 which is the same as 1-x=y
If x=0, y=1 (y intercept); if y=0, x=1 (x intercept). The sides are the distance from the origin to the x-intercept and the distance from the origin to the y-intercept; therefore, this line forms a right triangle with the x and y axes that has leg lengths of 1. The area of a triangle is (1/2)(bh). b and h, in this case, both equal 1, so area=1/2.</p>

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<p>Y=x+1, graph of y=x passes through the origin, raise the graph by one unit in the “y” direction and you form a triangle (-1, 0), (0, 0), (0, 1); the formula for the area of a triangle is 1/2bh = 0.5 in this case.</p>

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<p>The second one f (x) = root (x/11) sub in x = 2</p>