SOLUTION: I would appreciate it if someone could help with the following question: Solve the equation for 0 degrees<=x<=360 degrees. Express your answer as an exact value. 2tanx(cosx

Question 1058408: I would appreciate it if someone could help with the following question:
Solve the equation for 0 degrees<=x<=360 degrees. Express your answer as an exact value.
2tanx(cosx) - 1 = 0

Found 3 solutions by Alan3354, solve_for_x, stanbon:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
2tanx(cosx) - 1 = 0
---------
tan = sin/cos
---
--> 2sin(x) = 1
sin(x) = 1/2
etc
Answer by solve_for_x(190)   (Show Source): You can put this solution on YOUR website!
Since tan x = sin x / cos x, this equation can be rewritten as:

2(tan x)(cos x) - 1 = 0

2(sin x)(cos x)/(cos x) - 1 = 0

Canceling (cos x) from the first term leaves:

2(sin x) - 1 = 0

2(sin x) = 1

sin x = 1/2

x = arcsin(1/2)

x = 30 degrees, 150 degrees

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Solve the equation for 0 degrees<=x<=360 degrees. Express your answer as an exact value.
2tanx(cosx) - 1 = 0
--------------
tanx(cosx) = 1/2
----
Take the arctan of both sides to get:
cos(x) = 26.57 degrees or cos(x) = 180+26.57 degrees = 206.57 degrees
------------------
Comment: The cos (which is a ratio) cannot equal some number of degrees.
That does not make any sense.
Cheers,
Stan H.
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