Trig Equation (1 Viewer)

[Marc26]

Solve for 0 < theta < 360, giving solution to nearest minute where necessary:

 

[fortune_cookie]

2sin^2(x) -2sec(x) =8

 

[fortune_cookie]

sin^2(x) - sec(x) = 4

sin^2(x) - 1/cos(x) = 4

2sin^2(x) cos(x) - 1 = 4cos(x)

2(1-cos^2(x)) cos(x) -1 = 4cos(x)

2cos(x) - 2cos^3(x) -1 = 4cos(x)

2cos^3(x) +2cos(x) +1 =0

 

[Marc26]

sorry its the first attached jpg image

 

[hayabusaboston]

reducible to quadratic innit?

 

[hayabusaboston]

sorry its the first attached jpg image

2x^2-2x-8=0

Solve for x, then replace x with sin theta

 

[fortune_cookie]

sin^2(x) - sin(x) = 4

sin^2(x) -sin(x) -4 =0

We need two numbers that multiply to give (1*-4) =-4 , and add to give -1

-4 & +1

sin^2(x) +sin(x) -4sin(x)-4 =0

sin(x) [ sin(x) +1] -4[ sin(x) +1] =0

[sin(x)+1] [sin(x)-4]=0

sin(x) =-1 or sin(x) =4

sin(x) =-1 ---> x= (3pi)/2 // from a graph.

sin(x) =4 ---> No SOLN as the range of sin(x) is -1<=sin(x)<=1

x=(3pi)/2 is only soln.

 

[fortune_cookie]

Ignore that :|.

There is a problem with it and unforunately I cannot edit it. Damn slow internet. :|

 

[Fus Ro Dah]

sin^2(x) - sin(x) = 4

sin^2(x) -sin(x) -4 =0

We need two numbers that multiply to give (1*-4) =-4 , and add to give -1

-4 & +1

sin^2(x) +sin(x) -4sin(x)-4 =0

sin(x) [ sin(x) +1] -4[ sin(x) +1] =0

[sin(x)+1] [sin(x)-4]=0

sin(x) =-1 or sin(x) =4

sin(x) =-1 ---> x= (3pi)/2 // from a graph.

sin(x) =4 ---> No SOLN as the range of sin(x) is -1<=sin(x)<=1

x=(3pi)/2 is only soln.

Since when did -4+1 = -1?

 

[hayabusaboston]

sin^2(x) - sin(x) = 4

sin^2(x) -sin(x) -4 =0

We need two numbers that multiply to give (1*-4) =-4 , and add to give -1

-4 & +1

sin^2(x) +sin(x) -4sin(x)-4 =0

sin(x) [ sin(x) +1] -4[ sin(x) +1] =0

[sin(x)+1] [sin(x)-4]=0

sin(x) =-1 or sin(x) =4

sin(x) =-1 ---> x= (3pi)/2 // from a graph.

sin(x) =4 ---> No SOLN as the range of sin(x) is -1<=sin(x)<=1

x=(3pi)/2 is only soln.

see i gave u good idea eh?

 

[Fus Ro Dah]

see i gave u good idea eh?

hayabusaboston, fortune_cookie is very competent with Mathematics, and I am very confident that he/she would have known what to do without your 'idea'.

 

[hayabusaboston]

hayabusaboston, fortune_cookie is very competent with Mathematics, and I am very confident that he/she would have known what to do without your 'idea'.

Of course I am not meaning to cause offense bro, just trying to be nice lol. Cos I noticed he/she was flipping around all these trig identities for no apparent reason.