how many solutions are there for the equation sinxcosx = 1/6

iamyourfather

New member
Joined
Sep 22, 2017
Messages
1
For x belongs to [2pi) how many solutions are there for the equation sinxcosx = 1/6?

I need steps of the question ;( Because I don't know how to write it .
Thank you

god bless
 
(sin2x = 2sinxcosx)
For x belongs to [ 0 , 2pi ) , how many solutions are there for the equation sinx cosx = 1/6

I need step of this question .
Thank you ;)
Father,

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33
 
Have you considered the suggested transformation? \(\displaystyle \sin(2x) = 2\sin(x)\cos(x)\) Very useful.
 
yup , I have considered the suggested transformation already ...
That is what I had done yesterday
View attachment 8533
you see , I know there are two solutions for the equation but I don't know how to write and express the final step now .
attachment.php

How can you show (prove) there are two solutions (in the given domain)?
 
Last edited by a moderator:
For x belongs to [2pi) how many solutions are there for the equation sinxcosx = 1/6?

I need steps of the question ;( Because I don't know how to write it .
Thank you

god bless
Suppose I do a different problem:

For x belongs to [2pi) how many solutions are there for the equation sinxcosx = 1/4?

sin(x) * cos(x) = 1/4

2 * sin(x) * cos(x) = 1/2

sin(2x) = 1/2

2x = 30°, 150°, 390°, 510°........

x = 15°, 75°, 195°, 255°,.....

So you observe that there are four solutions for above problem within the given domain.
 
Why did you delete your useful response? We wouldn't know how to help you without that.
 
Top