SOLUTION: please help me solve this equation: solve exactly: sin(x) + 4csc(x) + 5=0 I have done: sin(x) + 4/sin(x) +5=0 sin^2(x)/sin(x)+4/sin(x)+5+0

Question 1011901: please help me solve this equation: solve exactly: sin(x) + 4csc(x) + 5=0
I have done: sin(x) + 4/sin(x) +5=0
sin^2(x)/sin(x)+4/sin(x)+5+0
4+sin^2(x)/sin(x)=-5
4+sin^2(x)=-5sin(x)
sin^2(x)+5sin(x)+4=0
(sin(x)+1) (sin(x)+4) =0
sin(x)=-1, sin(x)=-4.
Please let me know if I have made a mistake somewhere, and/or where to go from here. I need to have an exact value, so I can't just plug in sin^-1(-1) and sin^-1(-4) into my calculator.
Thanks so much
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve exactly:
sin(x) + 4csc(x) + 5=0
------
Multiply thru by sin(x) to get:
sin^2(x) + 5sin(x) + 4 = 0
-----
Factor:
(sin(x)+1)(sin(x)+4) = 0
---
sin(x) = -1 or sin(x) = -4 (extraneous)
----
sin(x) = -1 when x = 270 degrees.
-----------
Cheers,
Stan H.
-----------
RELATED QUESTIONS
Solve sin^2 x + sin x + 4 = 0 for x. (answered by Shin123,math_tutor2020)

please help me solve:... (answered by jim_thompson5910)

solve the equation: sin x(sin x + 1) = 0 4 cos^2 x - 1 =... (answered by ewatrrr)

Please help me solve this equation! (a)Solve approximately the equations: (i)2 sin x +... (answered by KMST)

Solve... (answered by jim_thompson5910)

sin^2(x)+sin(x)=0 (answered by josgarithmetic)

Solve ; sin(x) sin(2x) < sin(3x) sin(4x) (answered by MowMow,Alan3354,ikleyn)

please help me solve sin(x) = sin(2x) interval... (answered by jim_thompson5910)