Question
solve the equation
1+4sin(x)=4cos^2(x)
1+4sin(x)=4cos^2(x)
Answers
bandit5571
without a graphing utility
Reiny
1+4sin(x)=4cos^2(x)
1+4sinx = 4(1 - sin^2 x)
4sin^2 x + 4sinx -3 = 0
(2sinx - 1)(2sinx + 3) = 0
sinx = 1/2 or sinx = -3/2
the last part is not possible since sinx is between -1 and +1
so sinx = 1/2
x must be in quadrants I or II
I know sin 30° = 1/2
so x = 30° or 150°
in radians
x = π/6 or x = 5π/6
1+4sinx = 4(1 - sin^2 x)
4sin^2 x + 4sinx -3 = 0
(2sinx - 1)(2sinx + 3) = 0
sinx = 1/2 or sinx = -3/2
the last part is not possible since sinx is between -1 and +1
so sinx = 1/2
x must be in quadrants I or II
I know sin 30° = 1/2
so x = 30° or 150°
in radians
x = π/6 or x = 5π/6