SOLUTION: Find all solutions of the equation on the interval [0,2pi) -4sinx = -cos^2x+4 Write answer in terms of pi

Question 1160202: Find all solutions of the equation on the interval [0,2pi)
-4sinx = -cos^2x+4
Write answer in terms of pi
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Find all solutions of the equation on the interval [,)

............use the following identity :

......both sides multiply by
.........let
.......factor

solutions:

substitute back
-> general solutions for :
for interval will be =>
-> can't be smaller than for real solutions => no solution exist

Answer by ikleyn(52872) (Show Source): You can put this solution on YOUR website!
.

-4sin(x) = -cos^2(x) + 4 Replace cos^2(x) by 1 - sin^2(x). You will get -4sin(x) = -(1-sin^2(x)) + 4 sin^2(x) + 4sin(x)x + 3 = 0 Factor (sin(x) + 3)*(sin(x) + 1) = 0 The only real solution is sin(x) = -1, which gives x = . ANSWER Plot y = -4sin(x) (red) and y = -cos^2(x) +4 (green)

RELATED QUESTIONS
Find all solutions of the equation in the interval [0, 2pi). -sinx=-cos^2x-1 Write... (answered by Alan3354)
Find all solutions of the equation in the interval [0, 2pi). -4 cos x =-sin^2(x)+4... (answered by josgarithmetic)
Find all solutions of the equation in the interval [0, 2pi). secTHETA + sqrt 2 = 0 (answered by Alan3354)
Find all solutions of each of the equations in the interval (0, 2pi) cos(x- pi/2) +... (answered by lwsshak3)
Find all solutions of the equation in the interval (0,2π) 4cos^2x=5-4sinx (answered by Fombitz)
Find all solutions of the equation in interval [0,2) sinx=-cos^2x-1 Write answers in... (answered by Alan3354)
find all the solutions in the interval 0-x-2pi of the equation 2cos(squared)x+1 = 5sinx (answered by Fombitz)
Find all solutions of the equation in the interval [0, 2pi)... (answered by lwsshak3)
Find all solutions of the equation in the interval [0, 2pi).... (answered by Alan3354)