Write down two values of $k$ for which the equation $f(x)=k$ has exactly two solutions.
$begingroup$
$f(x)=5sin(x+0.927)$
It was also written in another form as $3sin x+4cos x$.
I understand that for $k$ to have no solutions, the range would be $|k|>5$.
But this question confused me, because it asked for specific values rather than a range, and I assume it asks for two solutions for EACH answer of $k$.
Thanks in advance!
trigonometry
edited Dec 17 '18 at 9:55
user334732
4,30211240
asked Dec 17 '18 at 9:48
ShioriShiori
1
$endgroup$
add a comment |
$begingroup$
$f(x)=5sin(x+0.927)$
It was also written in another form as $3sin x+4cos x$.
I understand that for $k$ to have no solutions, the range would be $|k|>5$.
But this question confused me, because it asked for specific values rather than a range, and I assume it asks for two solutions for EACH answer of $k$.
Thanks in advance!
trigonometry
edited Dec 17 '18 at 9:55
user334732
4,30211240
asked Dec 17 '18 at 9:48
ShioriShiori
1
$endgroup$
2
$begingroup$
What's restriction on $x$-- in $[0,2pi]$? I ask since $f$ is periodic, so if one solution infinitely many.
$endgroup$
– coffeemath
Dec 17 '18 at 9:53
$begingroup$
Hi, and welcome to MSE. Try writing your maths with this: math.meta.stackexchange.com/questions/5020/… I've done it for you on this occasion.
$endgroup$
– user334732
Dec 17 '18 at 9:54
$begingroup$
The restriction is -2pi to 2pi. Sorry for that confusion.
$endgroup$
– Shiori
Dec 18 '18 at 10:53
add a comment |
$begingroup$
$f(x)=5sin(x+0.927)$
It was also written in another form as $3sin x+4cos x$.
I understand that for $k$ to have no solutions, the range would be $|k|>5$.
But this question confused me, because it asked for specific values rather than a range, and I assume it asks for two solutions for EACH answer of $k$.
Thanks in advance!
trigonometry
edited Dec 17 '18 at 9:55
user334732
4,30211240
asked Dec 17 '18 at 9:48
ShioriShiori
1
$endgroup$
$f(x)=5sin(x+0.927)$
It was also written in another form as $3sin x+4cos x$.
I understand that for $k$ to have no solutions, the range would be $|k|>5$.
But this question confused me, because it asked for specific values rather than a range, and I assume it asks for two solutions for EACH answer of $k$.
Thanks in advance!
trigonometry
trigonometry
edited Dec 17 '18 at 9:55
user334732
4,30211240
asked Dec 17 '18 at 9:48
ShioriShiori
1
edited Dec 17 '18 at 9:55
user334732
4,30211240
asked Dec 17 '18 at 9:48
ShioriShiori
1
edited Dec 17 '18 at 9:55
user334732
4,30211240
edited Dec 17 '18 at 9:55
user334732
4,30211240
edited Dec 17 '18 at 9:55
user334732
4,30211240
4,30211240
asked Dec 17 '18 at 9:48
ShioriShiori
1
asked Dec 17 '18 at 9:48
ShioriShiori
1
asked Dec 17 '18 at 9:48
ShioriShiori
1
1
2
$begingroup$
What's restriction on $x$-- in $[0,2pi]$? I ask since $f$ is periodic, so if one solution infinitely many.
$endgroup$
– coffeemath
Dec 17 '18 at 9:53
$begingroup$
Hi, and welcome to MSE. Try writing your maths with this: math.meta.stackexchange.com/questions/5020/… I've done it for you on this occasion.
$endgroup$
– user334732
Dec 17 '18 at 9:54
$begingroup$
The restriction is -2pi to 2pi. Sorry for that confusion.
$endgroup$
– Shiori
Dec 18 '18 at 10:53
add a comment |
2
$begingroup$
What's restriction on $x$-- in $[0,2pi]$? I ask since $f$ is periodic, so if one solution infinitely many.
$endgroup$
– coffeemath
Dec 17 '18 at 9:53
$begingroup$
Hi, and welcome to MSE. Try writing your maths with this: math.meta.stackexchange.com/questions/5020/… I've done it for you on this occasion.
$endgroup$
– user334732
Dec 17 '18 at 9:54
$begingroup$
The restriction is -2pi to 2pi. Sorry for that confusion.
$endgroup$
– Shiori
Dec 18 '18 at 10:53
2
2
$begingroup$
What's restriction on $x$-- in $[0,2pi]$? I ask since $f$ is periodic, so if one solution infinitely many.
$endgroup$
– coffeemath
Dec 17 '18 at 9:53
$begingroup$
What's restriction on $x$-- in $[0,2pi]$? I ask since $f$ is periodic, so if one solution infinitely many.
$endgroup$
– coffeemath
Dec 17 '18 at 9:53
$begingroup$
Hi, and welcome to MSE. Try writing your maths with this: math.meta.stackexchange.com/questions/5020/… I've done it for you on this occasion.
$endgroup$
– user334732
Dec 17 '18 at 9:54
$begingroup$
Hi, and welcome to MSE. Try writing your maths with this: math.meta.stackexchange.com/questions/5020/… I've done it for you on this occasion.
$endgroup$
– user334732
Dec 17 '18 at 9:54
$begingroup$
The restriction is -2pi to 2pi. Sorry for that confusion.
$endgroup$
– Shiori
Dec 18 '18 at 10:53
$begingroup$
The restriction is -2pi to 2pi. Sorry for that confusion.
$endgroup$
– Shiori
Dec 18 '18 at 10:53
add a comment |
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$begingroup$
What's restriction on $x$-- in $[0,2pi]$? I ask since $f$ is periodic, so if one solution infinitely many.
$endgroup$
– coffeemath
Dec 17 '18 at 9:53
$begingroup$
Hi, and welcome to MSE. Try writing your maths with this: math.meta.stackexchange.com/questions/5020/… I've done it for you on this occasion.
$endgroup$
– user334732
Dec 17 '18 at 9:54
$begingroup$
The restriction is -2pi to 2pi. Sorry for that confusion.
$endgroup$
– Shiori
Dec 18 '18 at 10:53