Question

Solve cos x tan x=1/2 for x over the interval [0,2 pi).
a. pi/6
b. pi/3 and 5pi/3
c. pi/6 and 11pi/6
d. pi/6 and 5pi/6

please help me:(

Answer 1

\[\cos x \tan x=\frac{ 1 }{ 2 },\cos x \frac{ \sin x }{ \cos x }=\frac{ 1 }{ 2 }\]
\[\sin x=\frac{ 1 }{ 2 }=\sin \frac{ \pi }{ 6 },\sin \left( \pi-\frac{ \pi }{ 6 } \right),x=\frac{ \pi }{ 6 },\frac{ 5 \pi }{ 6 }\]

Answer 2

cos x tan x=1/2
tan x can be written as sin x /cos x.
cos x (tan x)=1/2
cos x (sin x/cos x) =1/2
sin x =1/2
x = pi/6
General solution: x = npi+(-1)^n(pi/6)
At n = 0
x =pi/6
At n = 1
x =pi -(pi/6) =5pi/6
Source: http://www.mathskey.com/question2answer/

Answer 3

my teacher tried explaining that to me and i could never understand it but thanks i have a pretty ok idea about it...THANKS!!!!