list all x intercepts for y= -3sin(1/2x + 1/5 pi) on the interval [-2/5pi,4pi]

Question

anonymous · Answer

substitute y = 0

anonymous · Answer

did that and got stuck :-)

anonymous · Answer

good idea satellite - i'm getting a nice cold beer now!

anonymous · Answer

sin (x/2 + pi/5)=0
what are all the possible values of theta for sin theta = 0?

anonymous · Answer

how come you removed the -3 from sin?

anonymous · Answer

y = 0 = -3sin(1/2x + 1/5 pi) 
-3(1/2x + 1/5 pi) = 0
divide by 3 on both sides
sin(1/2x + 1/5 pi)=0

anonymous · Answer

I got x= 5.03, -1.26, 11.31

anonymous · Answer

ok, thanks! loophole can you please show me how

anonymous · Answer

I am really struggling with this one

anonymous · Answer

I used a program called Geogebra, so I didn't get it algebraically sorry, but you can check your answers with that. I'll try it now though.

myininaya · Answer

i got 18pi/5, 8pi/5,-2pi/5

anonymous · Answer

myininaya our answers are equal

anonymous · Answer

you should get 5 answers for the interval specified.

anonymous · Answer

that is one of the answers: i am more concerned with understanding why - thanks everyone so much!

myininaya · Answer

if you can read it this is what dhatraditya was trying to explain above

anonymous · Answer

can;t be 5 answers; the max in the range of answers is 3

anonymous · Answer

there are only 3

anonymous · Answer

how is that? there will be one at 0,pi,2pi,3pi and 4pi

myininaya · Answer

when i did 3pi dhatraditya i got someing over 4pi for the answer

anonymous · Answer

the range part of the question

anonymous · Answer

wait, the interval is specified for the angles that the sin value can take or the resultant Y can take?

anonymous · Answer

thank you so much myninaya! that is perfect!!!! can some one please recommend a decent place for me to brush up on unit circle trig

myininaya · Answer

x is between -2pi/5 and4pi
when i did theta =4pi , x was bigger than 4pi

myininaya · Answer

thetha=3pi*

anonymous · Answer

oh I see. silly me,.

myininaya · Answer

so we have only 3 solutions

anonymous · Answer

how would the answer change if sin were replaced by cos?

myininaya · Answer

i eat dhartrad got this right?

anonymous · Answer

not much, your angles would become pi/2, 3pi/2 and so on

anonymous · Answer

@myininaya. yup, got it.

anonymous · Answer

you guys are fantastic! Im going to post it now with cos :-)