Find all values of x in the interval of [0 degrees, 360 degrees] that satisfy this equation
2 sin x =cos x
show the steps please!
2007-11-07 16:17:28 · 4 answers · asked by Nicky 2 in Science & Mathematics ➔ Mathematics
2sin(x) = cos(x)
Divide both sides by cos(x)
2sin(x)/cos(x) = 1
2tan(x) = 1
tan(x) = 1/2
x = 26.57°
tan(x+180°) = tan(x)
x = 180° + 26.57° will also be a solution
x = 206.57° is a solution
x = {26.57°, 206.57°}
2007-11-07 16:22:15 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋
simplify first
2 tan x = 1
tan x = 1/2
tan^-1 (1/2) = x
x = 26.565 degrees
also add 180 you get the 2nd answer
26.565 + 180 = 206.565
2007-11-08 00:26:32 · answer #2 · answered by Tuan@GGHS 2 · 0⤊ 0⤋
2 sin x = cos x
2 (sin x)/(cos x) = 1
tan x = 1/2
x = 0.4636 or x = 3.6052
2007-11-08 00:22:04 · answer #3 · answered by Philo 7 · 0⤊ 0⤋
2 sin x = cos x
--------------------
cos x
2tanx = 1
tan x = 1/2
x = 26.56, 206.56
2007-11-08 00:20:27 · answer #4 · answered by Mαtt 6 · 0⤊ 0⤋