Find all solutions of the equation in the interval [0, 2pi).

Question

-4sinx=-cos^2(x)+4. That is cosine square times x plus 4.

write the answer in radians in term of pi.

Answer 1

x= 3pi/2

-4sinx = -cos^2(x) + 4

-4sin(3pi/2) = cos^2(3pi/2) +4

-4(-1) = 0^2 +4

4 =0 + 4

-4sinx = -cos^2(x) +4

-4sinx = -1+sin^2(x) +4

sin^2(x) +4sinx +3 = 0

(sinx +3)(sinx+1) = 0

sinx =-1 or -3 (ignore -3 as it's impossible)

x = 3pi/2