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Number of solutions of $2^cos x=|sin x|$
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I have tried a lot on solving this question, but i m unable to simplify the expression.
Find the total number of solutions of $2^cos x=|sin x|$ where $xin[-2À,5À]$.
See the answer below for the OP's thoughts.
functions trigonometry
edited Jul 25 at 4:42
Jyrki Lahtonen
104k12161355
asked Jul 25 at 3:51
user199925
194
add a comment |Â
up vote
0
down vote
favorite
I have tried a lot on solving this question, but i m unable to simplify the expression.
Find the total number of solutions of $2^cos x=|sin x|$ where $xin[-2À,5À]$.
See the answer below for the OP's thoughts.
functions trigonometry
edited Jul 25 at 4:42
Jyrki Lahtonen
104k12161355
asked Jul 25 at 3:51
user199925
194
1
It cannot be simplified. Did you plot the two functions to get an idea?
– Jyrki Lahtonen
Jul 25 at 3:56
Hint: there's a solution at $pi/2$. Second hint: both are even functions.
– Joffan
Jul 25 at 3:59
4
Also, I recommend that you study our guide to new askers. The way your question is written, brief and to the point as it is, presses people's buttons here because it has the air of trying to outsource homework. Take my first comment as one way of providing additional context and sharing your own thoughts.
– Jyrki Lahtonen
Jul 25 at 3:59
@Jyrki Excellent way of putting it! I've been having a hard time expressing that feeling
– Sambo
Jul 25 at 4:24
Thank you Jyrki for your support, I'll surely read that guide, coz I m new here
– user199925
Jul 25 at 4:31
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have tried a lot on solving this question, but i m unable to simplify the expression.
Find the total number of solutions of $2^cos x=|sin x|$ where $xin[-2À,5À]$.
See the answer below for the OP's thoughts.
functions trigonometry
edited Jul 25 at 4:42
Jyrki Lahtonen
104k12161355
asked Jul 25 at 3:51
user199925
194
I have tried a lot on solving this question, but i m unable to simplify the expression.
Find the total number of solutions of $2^cos x=|sin x|$ where $xin[-2À,5À]$.
See the answer below for the OP's thoughts.
functions trigonometry
edited Jul 25 at 4:42
Jyrki Lahtonen
104k12161355
asked Jul 25 at 3:51
user199925
194
edited Jul 25 at 4:42
Jyrki Lahtonen
104k12161355
edited Jul 25 at 4:42
Jyrki Lahtonen
104k12161355
edited Jul 25 at 4:42
Jyrki Lahtonen
104k12161355
104k12161355
asked Jul 25 at 3:51
user199925
194
asked Jul 25 at 3:51
user199925
194
asked Jul 25 at 3:51
user199925
194
194
1
It cannot be simplified. Did you plot the two functions to get an idea?
– Jyrki Lahtonen
Jul 25 at 3:56
Hint: there's a solution at $pi/2$. Second hint: both are even functions.
– Joffan
Jul 25 at 3:59
4
Also, I recommend that you study our guide to new askers. The way your question is written, brief and to the point as it is, presses people's buttons here because it has the air of trying to outsource homework. Take my first comment as one way of providing additional context and sharing your own thoughts.
– Jyrki Lahtonen
Jul 25 at 3:59
@Jyrki Excellent way of putting it! I've been having a hard time expressing that feeling
– Sambo
Jul 25 at 4:24
Thank you Jyrki for your support, I'll surely read that guide, coz I m new here
– user199925
Jul 25 at 4:31
add a comment |Â
1
It cannot be simplified. Did you plot the two functions to get an idea?
– Jyrki Lahtonen
Jul 25 at 3:56
Hint: there's a solution at $pi/2$. Second hint: both are even functions.
– Joffan
Jul 25 at 3:59
4
Also, I recommend that you study our guide to new askers. The way your question is written, brief and to the point as it is, presses people's buttons here because it has the air of trying to outsource homework. Take my first comment as one way of providing additional context and sharing your own thoughts.
– Jyrki Lahtonen
Jul 25 at 3:59
@Jyrki Excellent way of putting it! I've been having a hard time expressing that feeling
– Sambo
Jul 25 at 4:24
Thank you Jyrki for your support, I'll surely read that guide, coz I m new here
– user199925
Jul 25 at 4:31
1
1
It cannot be simplified. Did you plot the two functions to get an idea?
– Jyrki Lahtonen
Jul 25 at 3:56
It cannot be simplified. Did you plot the two functions to get an idea?
– Jyrki Lahtonen
Jul 25 at 3:56
Hint: there's a solution at $pi/2$. Second hint: both are even functions.
– Joffan
Jul 25 at 3:59
Hint: there's a solution at $pi/2$. Second hint: both are even functions.
– Joffan
Jul 25 at 3:59
4
4
Also, I recommend that you study our guide to new askers. The way your question is written, brief and to the point as it is, presses people's buttons here because it has the air of trying to outsource homework. Take my first comment as one way of providing additional context and sharing your own thoughts.
– Jyrki Lahtonen
Jul 25 at 3:59
Also, I recommend that you study our guide to new askers. The way your question is written, brief and to the point as it is, presses people's buttons here because it has the air of trying to outsource homework. Take my first comment as one way of providing additional context and sharing your own thoughts.
– Jyrki Lahtonen
Jul 25 at 3:59
@Jyrki Excellent way of putting it! I've been having a hard time expressing that feeling
– Sambo
Jul 25 at 4:24
@Jyrki Excellent way of putting it! I've been having a hard time expressing that feeling
– Sambo
Jul 25 at 4:24
Thank you Jyrki for your support, I'll surely read that guide, coz I m new here
– user199925
Jul 25 at 4:31
Thank you Jyrki for your support, I'll surely read that guide, coz I m new here
– user199925
Jul 25 at 4:31
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
2
down vote
Sorry to bother you guys I finally did it myself
The graph of 2^cosx will cut |sin x| two times in interval of À , so total solutions will be 2×(5+2)= 14.
ðŸ˜ÂðŸ˜ÂðŸ˜ÂðŸ˜Â
answered Jul 25 at 4:27
user199925
194
Presumably you mean in an interval of the form $[npi,(n+1)pi]$. Good job, you see it wasn't too hard! Now, depending on the course you are in, it may or may not be expected that you justify this observation. By properties of continuous functions you can (a bit more rigorously) show that there are at least this many solutions. To prove that there are no more solutions you (probably) need to bring in the concepts of increasing/decreasing functions, or derivatives. It is still difficult for us to tell whether that is expected. Because we know nothing about the course you are in:-) Tell us!
– Jyrki Lahtonen
Jul 25 at 4:35
I m currently in class 12th and studying for competitive exams
– user199925
Jul 25 at 5:06
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
Sorry to bother you guys I finally did it myself
The graph of 2^cosx will cut |sin x| two times in interval of À , so total solutions will be 2×(5+2)= 14.
ðŸ˜ÂðŸ˜ÂðŸ˜ÂðŸ˜Â
answered Jul 25 at 4:27
user199925
194
Presumably you mean in an interval of the form $[npi,(n+1)pi]$. Good job, you see it wasn't too hard! Now, depending on the course you are in, it may or may not be expected that you justify this observation. By properties of continuous functions you can (a bit more rigorously) show that there are at least this many solutions. To prove that there are no more solutions you (probably) need to bring in the concepts of increasing/decreasing functions, or derivatives. It is still difficult for us to tell whether that is expected. Because we know nothing about the course you are in:-) Tell us!
– Jyrki Lahtonen
Jul 25 at 4:35
I m currently in class 12th and studying for competitive exams
– user199925
Jul 25 at 5:06
add a comment |Â
up vote
2
down vote
Sorry to bother you guys I finally did it myself
The graph of 2^cosx will cut |sin x| two times in interval of À , so total solutions will be 2×(5+2)= 14.
ðŸ˜ÂðŸ˜ÂðŸ˜ÂðŸ˜Â
answered Jul 25 at 4:27
user199925
194
Presumably you mean in an interval of the form $[npi,(n+1)pi]$. Good job, you see it wasn't too hard! Now, depending on the course you are in, it may or may not be expected that you justify this observation. By properties of continuous functions you can (a bit more rigorously) show that there are at least this many solutions. To prove that there are no more solutions you (probably) need to bring in the concepts of increasing/decreasing functions, or derivatives. It is still difficult for us to tell whether that is expected. Because we know nothing about the course you are in:-) Tell us!
– Jyrki Lahtonen
Jul 25 at 4:35
I m currently in class 12th and studying for competitive exams
– user199925
Jul 25 at 5:06
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Sorry to bother you guys I finally did it myself
The graph of 2^cosx will cut |sin x| two times in interval of À , so total solutions will be 2×(5+2)= 14.
ðŸ˜ÂðŸ˜ÂðŸ˜ÂðŸ˜Â
answered Jul 25 at 4:27
user199925
194
Sorry to bother you guys I finally did it myself
The graph of 2^cosx will cut |sin x| two times in interval of À , so total solutions will be 2×(5+2)= 14.
ðŸ˜ÂðŸ˜ÂðŸ˜ÂðŸ˜Â
answered Jul 25 at 4:27
user199925
194
edited Jul 25 at 5:08
answered Jul 25 at 4:27
user199925
194
answered Jul 25 at 4:27
user199925
194
answered Jul 25 at 4:27
user199925
194
194
Presumably you mean in an interval of the form $[npi,(n+1)pi]$. Good job, you see it wasn't too hard! Now, depending on the course you are in, it may or may not be expected that you justify this observation. By properties of continuous functions you can (a bit more rigorously) show that there are at least this many solutions. To prove that there are no more solutions you (probably) need to bring in the concepts of increasing/decreasing functions, or derivatives. It is still difficult for us to tell whether that is expected. Because we know nothing about the course you are in:-) Tell us!
– Jyrki Lahtonen
Jul 25 at 4:35
I m currently in class 12th and studying for competitive exams
– user199925
Jul 25 at 5:06
add a comment |Â
Presumably you mean in an interval of the form $[npi,(n+1)pi]$. Good job, you see it wasn't too hard! Now, depending on the course you are in, it may or may not be expected that you justify this observation. By properties of continuous functions you can (a bit more rigorously) show that there are at least this many solutions. To prove that there are no more solutions you (probably) need to bring in the concepts of increasing/decreasing functions, or derivatives. It is still difficult for us to tell whether that is expected. Because we know nothing about the course you are in:-) Tell us!
– Jyrki Lahtonen
Jul 25 at 4:35
I m currently in class 12th and studying for competitive exams
– user199925
Jul 25 at 5:06
Presumably you mean in an interval of the form $[npi,(n+1)pi]$. Good job, you see it wasn't too hard! Now, depending on the course you are in, it may or may not be expected that you justify this observation. By properties of continuous functions you can (a bit more rigorously) show that there are at least this many solutions. To prove that there are no more solutions you (probably) need to bring in the concepts of increasing/decreasing functions, or derivatives. It is still difficult for us to tell whether that is expected. Because we know nothing about the course you are in:-) Tell us!
– Jyrki Lahtonen
Jul 25 at 4:35
Presumably you mean in an interval of the form $[npi,(n+1)pi]$. Good job, you see it wasn't too hard! Now, depending on the course you are in, it may or may not be expected that you justify this observation. By properties of continuous functions you can (a bit more rigorously) show that there are at least this many solutions. To prove that there are no more solutions you (probably) need to bring in the concepts of increasing/decreasing functions, or derivatives. It is still difficult for us to tell whether that is expected. Because we know nothing about the course you are in:-) Tell us!
– Jyrki Lahtonen
Jul 25 at 4:35
I m currently in class 12th and studying for competitive exams
– user199925
Jul 25 at 5:06
I m currently in class 12th and studying for competitive exams
– user199925
Jul 25 at 5:06
add a comment |Â
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1
It cannot be simplified. Did you plot the two functions to get an idea?
– Jyrki Lahtonen
Jul 25 at 3:56
Hint: there's a solution at $pi/2$. Second hint: both are even functions.
– Joffan
Jul 25 at 3:59
4
Also, I recommend that you study our guide to new askers. The way your question is written, brief and to the point as it is, presses people's buttons here because it has the air of trying to outsource homework. Take my first comment as one way of providing additional context and sharing your own thoughts.
– Jyrki Lahtonen
Jul 25 at 3:59
@Jyrki Excellent way of putting it! I've been having a hard time expressing that feeling
– Sambo
Jul 25 at 4:24
Thank you Jyrki for your support, I'll surely read that guide, coz I m new here
– user199925
Jul 25 at 4:31