Solution of Trig equation $sin x+2cos x=1+sqrt3cos x$ The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Find the smallest positive number $p$ for which the equation $cos(psin x)=sin(p cos x)$ has a solution $xin[0,2pi].$General Solution of the equation $sin^2015(phi)+cos^2015(phi) = 1$Number of solutions of $8sin(x)=fracsqrt3cos(x)+frac1sin(x)$How many solutions exist for the equation $2sin(x)+cos(x)=sqrt3$ in $[0,2pi]$?Finding smallest positive root $sqrtsin(1-x)=sqrtcos x$number of distinct solution $xin[0,pi]$ of the equation satisfy $8cos xcos 4xcos 5x=1$Solution of $sqrtcot(3x)+sin^2(x)-frac14+sqrtsqrt3cos x+sin x-2=sinleft(frac3x2right)-frac1sqrt2$Real solution of $(cos x -sin x)cdot bigg(2tan x+frac1cos xbigg)+2=0.$If $cos^4 alpha+4sin^4 beta-4sqrt2cos alpha sin beta +2=0$, then find $alpha$, $beta$ in $(0,fracpi2)$If the equation $sin^2x-asin x+b=0$ has only one solution in $(0,pi)$, then what is the range of $b$?
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Solution of Trig equation $sin x+2cos x=1+sqrt3cos x$
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Find the smallest positive number $p$ for which the equation $cos(psin x)=sin(p cos x)$ has a solution $xin[0,2pi].$General Solution of the equation $sin^2015(phi)+cos^2015(phi) = 1$Number of solutions of $8sin(x)=fracsqrt3cos(x)+frac1sin(x)$How many solutions exist for the equation $2sin(x)+cos(x)=sqrt3$ in $[0,2pi]$?Finding smallest positive root $sqrtsin(1-x)=sqrtcos x$number of distinct solution $xin[0,pi]$ of the equation satisfy $8cos xcos 4xcos 5x=1$Solution of $sqrtcot(3x)+sin^2(x)-frac14+sqrtsqrt3cos x+sin x-2=sinleft(frac3x2right)-frac1sqrt2$Real solution of $(cos x -sin x)cdot bigg(2tan x+frac1cos xbigg)+2=0.$If $cos^4 alpha+4sin^4 beta-4sqrt2cos alpha sin beta +2=0$, then find $alpha$, $beta$ in $(0,fracpi2)$If the equation $sin^2x-asin x+b=0$ has only one solution in $(0,pi)$, then what is the range of $b$?
$begingroup$
The sum of all solution of the equation
$sin x+2cos x=1+sqrt3cos x$ in $[0,2pi]$
My Try:
$$(sin x+cos x)+(sin x-sqrt3cos x)=1$$
$$sqrt2sin bigg(x+fracpi4bigg)+2sin bigg(x-fracpi3bigg)=1$$
Could some Help me to solve it. Thanks in Advance
trigonometry
asked Mar 31 at 14:46
DXTDXT
5,8742733
$endgroup$
add a comment |
$begingroup$
The sum of all solution of the equation
$sin x+2cos x=1+sqrt3cos x$ in $[0,2pi]$
My Try:
$$(sin x+cos x)+(sin x-sqrt3cos x)=1$$
$$sqrt2sin bigg(x+fracpi4bigg)+2sin bigg(x-fracpi3bigg)=1$$
Could some Help me to solve it. Thanks in Advance
trigonometry
asked Mar 31 at 14:46
DXTDXT
5,8742733
$endgroup$
$begingroup$
Your working shows an equation that is not the same as the original equation.
$endgroup$
– Peter Foreman
Mar 31 at 14:52
add a comment |
$begingroup$
The sum of all solution of the equation
$sin x+2cos x=1+sqrt3cos x$ in $[0,2pi]$
My Try:
$$(sin x+cos x)+(sin x-sqrt3cos x)=1$$
$$sqrt2sin bigg(x+fracpi4bigg)+2sin bigg(x-fracpi3bigg)=1$$
Could some Help me to solve it. Thanks in Advance
trigonometry
asked Mar 31 at 14:46
DXTDXT
5,8742733
$endgroup$
The sum of all solution of the equation
$sin x+2cos x=1+sqrt3cos x$ in $[0,2pi]$
My Try:
$$(sin x+cos x)+(sin x-sqrt3cos x)=1$$
$$sqrt2sin bigg(x+fracpi4bigg)+2sin bigg(x-fracpi3bigg)=1$$
Could some Help me to solve it. Thanks in Advance
trigonometry
trigonometry
asked Mar 31 at 14:46
DXTDXT
5,8742733
asked Mar 31 at 14:46
DXTDXT
5,8742733
edited Mar 31 at 14:53
DXT
asked Mar 31 at 14:46
DXTDXT
5,8742733
asked Mar 31 at 14:46
DXTDXT
5,8742733
asked Mar 31 at 14:46
DXTDXT
5,8742733
5,8742733
$begingroup$
Your working shows an equation that is not the same as the original equation.
$endgroup$
– Peter Foreman
Mar 31 at 14:52
add a comment |
$begingroup$
Your working shows an equation that is not the same as the original equation.
$endgroup$
– Peter Foreman
Mar 31 at 14:52
$begingroup$
Your working shows an equation that is not the same as the original equation.
$endgroup$
– Peter Foreman
Mar 31 at 14:52
$begingroup$
Your working shows an equation that is not the same as the original equation.
$endgroup$
– Peter Foreman
Mar 31 at 14:52
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
Remeber that we can write $$f(x)= asin x +bcos x $$ like this : $$f(x)=A sin (x+phi)$$
where $A= sqrta^2+b^2$ and $tan phi = b/a$.
So $$sin x+(2-sqrt3)cos x =1$$
$A = sqrt8-4sqrt3$ and $phi =
pi/12$
answered Mar 31 at 15:04
Maria MazurMaria Mazur
49.9k1361125
$endgroup$
add a comment |
$begingroup$
Hint: Substitute $$sin(x)=frac2t1+t^2$$
$$cos(x)=frac1-t^21+t^2$$
the so-called Weierstrass substitution
answered Mar 31 at 14:54
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79k42867
$endgroup$
add a comment |
$begingroup$
Set $X=cos x$ and $Y=sin x$; then $Y=1+(sqrt3-2)X$. Substitute into $X^2+Y^2=1$.
answered Mar 31 at 15:14
egregegreg
186k1486208
$endgroup$
add a comment |
$begingroup$
Hint:
$$2-sqrt3=csc30^circ-cot30^circ=tan15^circ=cot75^circ$$
If $$sin x+cot Acos x=1$$
$$cos(x-A)=sin A=cot(90^circ-A)$$
$x=?$
answered Mar 31 at 15:34
lab bhattacharjeelab bhattacharjee
228k15159279
$endgroup$
add a comment |
Your Answer
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Remeber that we can write $$f(x)= asin x +bcos x $$ like this : $$f(x)=A sin (x+phi)$$
where $A= sqrta^2+b^2$ and $tan phi = b/a$.
So $$sin x+(2-sqrt3)cos x =1$$
$A = sqrt8-4sqrt3$ and $phi =
pi/12$
answered Mar 31 at 15:04
Maria MazurMaria Mazur
49.9k1361125
$endgroup$
add a comment |
$begingroup$
Remeber that we can write $$f(x)= asin x +bcos x $$ like this : $$f(x)=A sin (x+phi)$$
where $A= sqrta^2+b^2$ and $tan phi = b/a$.
So $$sin x+(2-sqrt3)cos x =1$$
$A = sqrt8-4sqrt3$ and $phi =
pi/12$
answered Mar 31 at 15:04
Maria MazurMaria Mazur
49.9k1361125
$endgroup$
add a comment |
$begingroup$
Remeber that we can write $$f(x)= asin x +bcos x $$ like this : $$f(x)=A sin (x+phi)$$
where $A= sqrta^2+b^2$ and $tan phi = b/a$.
So $$sin x+(2-sqrt3)cos x =1$$
$A = sqrt8-4sqrt3$ and $phi =
pi/12$
answered Mar 31 at 15:04
Maria MazurMaria Mazur
49.9k1361125
$endgroup$
Remeber that we can write $$f(x)= asin x +bcos x $$ like this : $$f(x)=A sin (x+phi)$$
where $A= sqrta^2+b^2$ and $tan phi = b/a$.
So $$sin x+(2-sqrt3)cos x =1$$
$A = sqrt8-4sqrt3$ and $phi =
pi/12$
answered Mar 31 at 15:04
Maria MazurMaria Mazur
49.9k1361125
answered Mar 31 at 15:04
Maria MazurMaria Mazur
49.9k1361125
answered Mar 31 at 15:04
Maria MazurMaria Mazur
49.9k1361125
answered Mar 31 at 15:04
Maria MazurMaria Mazur
49.9k1361125
49.9k1361125
add a comment |
add a comment |
$begingroup$
Hint: Substitute $$sin(x)=frac2t1+t^2$$
$$cos(x)=frac1-t^21+t^2$$
the so-called Weierstrass substitution
answered Mar 31 at 14:54
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79k42867
$endgroup$
add a comment |
$begingroup$
Hint: Substitute $$sin(x)=frac2t1+t^2$$
$$cos(x)=frac1-t^21+t^2$$
the so-called Weierstrass substitution
answered Mar 31 at 14:54
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79k42867
$endgroup$
add a comment |
$begingroup$
Hint: Substitute $$sin(x)=frac2t1+t^2$$
$$cos(x)=frac1-t^21+t^2$$
the so-called Weierstrass substitution
answered Mar 31 at 14:54
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79k42867
$endgroup$
Hint: Substitute $$sin(x)=frac2t1+t^2$$
$$cos(x)=frac1-t^21+t^2$$
the so-called Weierstrass substitution
answered Mar 31 at 14:54
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79k42867
answered Mar 31 at 14:54
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79k42867
answered Mar 31 at 14:54
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79k42867
answered Mar 31 at 14:54
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79k42867
79k42867
add a comment |
add a comment |
$begingroup$
Set $X=cos x$ and $Y=sin x$; then $Y=1+(sqrt3-2)X$. Substitute into $X^2+Y^2=1$.
answered Mar 31 at 15:14
egregegreg
186k1486208
$endgroup$
add a comment |
$begingroup$
Set $X=cos x$ and $Y=sin x$; then $Y=1+(sqrt3-2)X$. Substitute into $X^2+Y^2=1$.
answered Mar 31 at 15:14
egregegreg
186k1486208
$endgroup$
add a comment |
$begingroup$
Set $X=cos x$ and $Y=sin x$; then $Y=1+(sqrt3-2)X$. Substitute into $X^2+Y^2=1$.
answered Mar 31 at 15:14
egregegreg
186k1486208
$endgroup$
Set $X=cos x$ and $Y=sin x$; then $Y=1+(sqrt3-2)X$. Substitute into $X^2+Y^2=1$.
answered Mar 31 at 15:14
egregegreg
186k1486208
answered Mar 31 at 15:14
egregegreg
186k1486208
answered Mar 31 at 15:14
egregegreg
186k1486208
answered Mar 31 at 15:14
egregegreg
186k1486208
186k1486208
add a comment |
add a comment |
$begingroup$
Hint:
$$2-sqrt3=csc30^circ-cot30^circ=tan15^circ=cot75^circ$$
If $$sin x+cot Acos x=1$$
$$cos(x-A)=sin A=cot(90^circ-A)$$
$x=?$
answered Mar 31 at 15:34
lab bhattacharjeelab bhattacharjee
228k15159279
$endgroup$
add a comment |
$begingroup$
Hint:
$$2-sqrt3=csc30^circ-cot30^circ=tan15^circ=cot75^circ$$
If $$sin x+cot Acos x=1$$
$$cos(x-A)=sin A=cot(90^circ-A)$$
$x=?$
answered Mar 31 at 15:34
lab bhattacharjeelab bhattacharjee
228k15159279
$endgroup$
add a comment |
$begingroup$
Hint:
$$2-sqrt3=csc30^circ-cot30^circ=tan15^circ=cot75^circ$$
If $$sin x+cot Acos x=1$$
$$cos(x-A)=sin A=cot(90^circ-A)$$
$x=?$
answered Mar 31 at 15:34
lab bhattacharjeelab bhattacharjee
228k15159279
$endgroup$
Hint:
$$2-sqrt3=csc30^circ-cot30^circ=tan15^circ=cot75^circ$$
If $$sin x+cot Acos x=1$$
$$cos(x-A)=sin A=cot(90^circ-A)$$
$x=?$
answered Mar 31 at 15:34
lab bhattacharjeelab bhattacharjee
228k15159279
answered Mar 31 at 15:34
lab bhattacharjeelab bhattacharjee
228k15159279
answered Mar 31 at 15:34
lab bhattacharjeelab bhattacharjee
228k15159279
answered Mar 31 at 15:34
lab bhattacharjeelab bhattacharjee
228k15159279
228k15159279
add a comment |
add a comment |
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$begingroup$
Your working shows an equation that is not the same as the original equation.
$endgroup$
– Peter Foreman
Mar 31 at 14:52