SOLUTION: This question has me really confused, hopefully you can help: Find all solutions of the equation [0,2pie) 2cos0-sqrt3=0 write your anwser in radians in terms of pie.

Algebra ->  Trigonometry-basics -> SOLUTION: This question has me really confused, hopefully you can help: Find all solutions of the equation [0,2pie) 2cos0-sqrt3=0 write your anwser in radians in terms of pie.      Log On


   

Question 1062656: This question has me really confused, hopefully you can help:
Find all solutions of the equation [0,2pie)
2cos0-sqrt3=0
write your anwser in radians in terms of pie.
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i think you mean cos(theta).
assuming that, i get:

2cos(theta) - sqrt(3) = 0
add sqrt(3) to both sides to get 2cos(theta) = sqrt(3)
divide both sides by 2 to get cos(theta) = sqrt(3)/2.

you want all solutions from 0 to 2pi.

that includes all 4 quadrants from 0 to 360 degrees.

cosine is positive in first and fourth quadrant.

therefore your solution is in the first quadrant and in the fourth quadrant.

it can't be in quadrants 2 and 3 because cosine is negative in those quadrants.

arccosine ((sqrt(3)/2) is equal to 30 degrees.

this is equivalent to 30 * pi / 180 = pi/6 radians.

this is in the first quadrant.

in the fourth quadrant this angle would be equal to 360 - 30 = 330 degrees.

this is equivalent to 330 * pi / 180 = 11pi/6 radians.

i believe your solution is that the angle in radians is equal to 1/6 * pi or 11/6 * pi radians.

that should be equivalent to 30 or 330 degrees

for graphing purposes, you would graph as follows:

graph the equation of y = 2cos(x)

on the same graph, graph the equation of y = sqrt(3).

the intersection of these 2 equations on that graph should be your solution.

alternatively, you should be able to graph y = 2cos(x) - sqrt(3) and your solution should be where y = 0.

the first 2 graphs show the solution in degrees.

the second 2 graphs show the solution in radians.

note that radians = degrees * pi / 180.

not that degrees = radians * 180 / pi.

not that sqrt(3) is equal to 1.732 rounded to 3 decimal digits.

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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
No math problems with pie.
---
Use the Greek letter pi.