Sat 2 Math level two problem?

Test Preparation SAT Subject Test Preparation
1

<p>The y-intercept of y= abs(2^(1/2)csc3(x+pi/5)) is </p>

<p>a.0.22
b.0.67
c.1.41
d.1.49
e.4.58 </p>

<p>The answer is 1.49 but i don't understand. I plug in 0 for x and put
abs(2^(1/2)(1/sin(pi/5)*3) but i get like 7.4 or something like that. </p>

<p>I think there is a typo at the back of the book because it says graph the plot
y=abs(2^(1/2)(1/sin(x+pi/5))) and find the value of x=0. That doesn't make snese at all cause it just disregarded the 3 completely and even with that, when i plotted it i got 2.4 or something similar to that.</p>

2

<p>my answer is 1.49.</p>

<p>all i did was type in (2^1/2)/sin (3pi/5) and i got 1.486. did you forget to convert you calculator to radian mode?</p>

3

<p>wait why does the 3 go inside the sin? It’s written on the outside</p>

4

<p>sin 3(0+pi/5)
= sin 3(pi/5)
= sin 3pi/5</p>

5

<p>doesn’t sin3(pi/5) = sin (pi/5) *3?</p>

<p>but when i put into my calculator, sin (pi/2)*3 does not equal sin(3pi/2)</p>

6

<p>that’s because ur calculator evaluates sin(pi/2) and then multiplies it by 3</p>

7

<p>doesn’t sin3(pi/5) = sin (pi/5) *3?</p>

<p>nope. sin (pi/5) *3 implies 3sin(pi/5). here 3 is the amplitude whereas in sin3(pi/5), it’s part of the period term.</p>

8

<p>if u still don’t get it, try graphing both. u’ll notice the difference. this is a particularly good site- [Trigonometric</a> Graphing](<a href=“Illuminations”>Trigonometric Graphing)</p>

9

<p>y=abs(2^(1/2)csc(3(x+pi/5))) (1)
Firstly, show that csc(3x) is not equal to 3csc(x):
Let x=pi/6.
Then
csc(3x)=1/sin(3x)=1/sin(3<em>pi/6)=1/sin(pi/2)=1/1=1.<br>
3csc(x)=3/sin(x)=3/sin(pi/6)=3/(1/2)=3</em>2=6.
To find the value where function f(x)= abs(2^(1/2)csc(3(x+pi/5))) intercepts “y”, we should substitute x=0 in (1).
We get y(0)=abs(2^(1/2)csc(3(0+pi/5)))=abs(2^(1/2)1/sin(3(pi/5)))=abs(2^(1/2)<em>1/(5/8+5^(1/2)/8)^(1/2))=abs(2^(1/2)</em>1.0515)=1.487=1.49.
Plot: y=abs(2^(1/2)csc(3(x+pi/5)))
<a href=“http://www4c.wolframalpha.com/Calculate/MSP/MSP18901c6if060a1h2icc400000eeff6adh8645c2a?MSPStoreType=image/gif&s=1&w=399.&h=192.&cdf=RangeControl[/url]”>http://www4c.wolframalpha.com/Calculate/MSP/MSP18901c6if060a1h2icc400000eeff6adh8645c2a?MSPStoreType=image/gif&s=1&w=399.&h=192.&cdf=RangeControl&lt;/a&gt;&lt;/p&gt;

<p><a href=“http://www4c.wolframalpha.com/Calculate/MSP/MSP18931c6if060a1h2icc4000051519g0h1hede267?MSPStoreType=image/gif&s=1&w=413.&h=192.&cdf=RangeControl[/url]”>http://www4c.wolframalpha.com/Calculate/MSP/MSP18931c6if060a1h2icc4000051519g0h1hede267?MSPStoreType=image/gif&s=1&w=413.&h=192.&cdf=RangeControl&lt;/a&gt;&lt;/p&gt;

10

<p>When we have to find the y-intercept, why are we setting the value of x=0 before graphing it?</p>

11

<p>We know that y-intercept is the value of y when x=0. Setting x=0 gives the y-intercept.</p>