A community for students.
Here's the question you clicked on:
 0 viewing
lgbasallote
 2 years ago
Find all values of x such that \(\sin 2x = \sin x\) and 0 < x < 2\(\pi\)
lgbasallote
 2 years ago
Find all values of x such that \(\sin 2x = \sin x\) and 0 < x < 2\(\pi\)

This Question is Closed

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0i suppose the only way for this to happen is if the x were 0....

JamesWolf
 2 years ago
Best ResponseYou've already chosen the best response.0yeah or pi, but you specified x < 2pi

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0hmm i suppose pi works

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0sin 2x = sin x arcsin both sides 2x = x 2x  x = 0 x = 0 how can i get the other values?

leedomathgeek
 2 years ago
Best ResponseYou've already chosen the best response.1sin(2x)=2sin(x)cos(x) Therefore, sin(2x)=sin(x) > 2sin(x)cos(x)=sin(x) 2sin(x)cos(x)sin(x)=0 sin(x)[2cos(x)1]=0 Now either sin(x)=0 > x=0,pi,... or 2cos(x)1=0 > cos(x)=1/2 > x=pi/3

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0then i suppose the others can be solved by adding pi?

leedomathgeek
 2 years ago
Best ResponseYou've already chosen the best response.1Why do you want to add a pi?

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0because one angle is missing

leedomathgeek
 2 years ago
Best ResponseYou've already chosen the best response.1You have only 3 solutions

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0there's actually 5.. but i know how to get one of the missing angles...

leedomathgeek
 2 years ago
Best ResponseYou've already chosen the best response.1oh ya i though x between 0 and pi

leedomathgeek
 2 years ago
Best ResponseYou've already chosen the best response.1sure 2pi is the 4th solution

leedomathgeek
 2 years ago
Best ResponseYou've already chosen the best response.1and x=2pip/3=5pi/3

leedomathgeek
 2 years ago
Best ResponseYou've already chosen the best response.1is the 5th solution

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.0oh subtract pi/3 from 2pi...ah yes... the negative angle

leedomathgeek
 2 years ago
Best ResponseYou've already chosen the best response.1exactly ...since cos(x) is positive in the 4th quad

apple_pi
 2 years ago
Best ResponseYou've already chosen the best response.0Here's an example you might want to look at: tan(4x) = tan(2x) 0° ≤ x ≤ 360° tan(4x) = tan(2x) ****DONT DO THIS: 4x = 2x INSTEAD... 4x = 180n 2x (Write one side as a general solution) then simplify: 6x = 180n x = 30n then you have all possible values of x now find all the ones that work, and you have all solutions
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.