Cos3x= square root of 3/2?

Question

I get confused on what to do with cos3x

James Adkins · Accepted Answer

#x=(pi/18)+(2npi)/3#

#x=(11pi)/18+(2npi)/3# #cos3x=sqrt3/2# Now, were there not a #3x# and it were just an #x,# we would just look for where #cosx=sqrt3/2#. In this case, it's not much different. Let's say #u=3x,# rewrite as #cosu=sqrt3/2# Okay, now for what #u# is this true? #u=pi/6+2npi# #u=(11pi)/6+2npi# Let's get back in terms of #x# #3x=pi/6+2npi# #3x=(11pi)/6+2npi# We need to solve for #x.# That's not really too bad, just divide both sides by three for each solution. #x=(pi/18)+(2npi)/3# #x=(11pi)/18+(2npi)/3#

Charles Autterson · Answer

# color(brown)(x = 10^@#

#cos 3x = sqrt3 / 2#

From the table above, #cos 30 = sqrt3 / 2#

#:. cos 3x = cos 30 = cos (3 * 10) #

#color(red)(cancel3) x = color(red)(cancel3) * 10, " or " color(brown)(x = 10^@#

Daniel Acosta · Answer

undefined To solve the equation cos(3x) = √3/2, you can use the inverse cosine function to find the values of x. Start by taking the inverse cosine of both sides of the equation:

cos^(-1)(cos(3x)) = cos^(-1)(√3/2)

This simplifies to:

3x = cos^(-1)(√3/2)

Now, you can solve for x by dividing both sides of the equation by 3:

x = (1/3) * cos^(-1)(√3/2)

This will give you the values of x that satisfy the equation. Keep in mind that the inverse cosine function typically gives values in the range [0, π], so you may need to consider multiple quadrants to find all possible solutions.