How to solve complicated equation for an argument of sine
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
I have an equation which was quite complicated in the begining and I have simplified it upto this point with multiple sine functions and I want to solve for an argument of sine i.e., $phi$,
$$sin(2k+phi)sin(3k+phi)+alphasin^2(2k+phi)+betasin^2ksin(3k+phi)csc(2k+phi)+Asin^2k=0$$
$alpha$, $beta$, $A$ are constants and $k$ is a variable (a number between $-pi$ to $pi$).
I guess if I try to use $sin(a+b)=sin acos b+cos asin b$ at this point, it becomes even more complicated, so is there any alternate trick to solve it for $phi$?
calculus real-analysis linear-algebra trigonometry
add a comment |Â
up vote
1
down vote
favorite
I have an equation which was quite complicated in the begining and I have simplified it upto this point with multiple sine functions and I want to solve for an argument of sine i.e., $phi$,
$$sin(2k+phi)sin(3k+phi)+alphasin^2(2k+phi)+betasin^2ksin(3k+phi)csc(2k+phi)+Asin^2k=0$$
$alpha$, $beta$, $A$ are constants and $k$ is a variable (a number between $-pi$ to $pi$).
I guess if I try to use $sin(a+b)=sin acos b+cos asin b$ at this point, it becomes even more complicated, so is there any alternate trick to solve it for $phi$?
calculus real-analysis linear-algebra trigonometry
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have an equation which was quite complicated in the begining and I have simplified it upto this point with multiple sine functions and I want to solve for an argument of sine i.e., $phi$,
$$sin(2k+phi)sin(3k+phi)+alphasin^2(2k+phi)+betasin^2ksin(3k+phi)csc(2k+phi)+Asin^2k=0$$
$alpha$, $beta$, $A$ are constants and $k$ is a variable (a number between $-pi$ to $pi$).
I guess if I try to use $sin(a+b)=sin acos b+cos asin b$ at this point, it becomes even more complicated, so is there any alternate trick to solve it for $phi$?
calculus real-analysis linear-algebra trigonometry
I have an equation which was quite complicated in the begining and I have simplified it upto this point with multiple sine functions and I want to solve for an argument of sine i.e., $phi$,
$$sin(2k+phi)sin(3k+phi)+alphasin^2(2k+phi)+betasin^2ksin(3k+phi)csc(2k+phi)+Asin^2k=0$$
$alpha$, $beta$, $A$ are constants and $k$ is a variable (a number between $-pi$ to $pi$).
I guess if I try to use $sin(a+b)=sin acos b+cos asin b$ at this point, it becomes even more complicated, so is there any alternate trick to solve it for $phi$?
calculus real-analysis linear-algebra trigonometry
edited Aug 23 at 4:21
asked Aug 23 at 4:06
AtoZ
64
64
add a comment |Â
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2891685%2fhow-to-solve-complicated-equation-for-an-argument-of-sine%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password