Question

Solve cos x tan x= 1/2 for x over the interval [0,2Pi]
A.) Pi/6
B.) Pi/3 and 5Pi/3
C.) Pi/6 and 11Pi/6
D.) Pi/6 and 5Pi/6

Answer 1

\(\color{#000000 }{ \displaystyle \tan x=\frac{ \sin x }{\cos x} }\)

therefore,

\(\color{#000000 }{ \displaystyle \cos x \tan x=\frac{\cos x \sin x }{\cos x} =\frac{\bcancel{\cos x} \sin x }{\bcancel{\cos x}} }\)

Answer 2

So, cosines are going to be cancelled \(....\)
However, you'll have to exclude any solutions for which \(\color{black}{\cos x=0}\).

Answer 3

(not that any solutions will have \(\color{black}{\cos x=0}\))

Answer 4

I'm still kinda lost. Is it B- \[\frac{ \Pi }{ 3 } and \frac{ 5\Pi }{ 3 }\]

Answer 5

@SolomonZelman

Answer 6

@roadjester - Is my answer correct? Can you help me, please? Im horrible with Algebra II/ Trig

Answer 7

Please, show your work that allowed you to arrive at yout answer.

Answer 8

@TheMadden5 do you know the answer ?

Answer 9

so than you know that sin30° = 1/2

- what will be the right answer ?

Answer 10

Ive figured it out. Thanks for helping everyone!