Question

Find all the solutions of the equation for the specified interval: \( 4 \cos ^{2}(x)-3=0 \) on \( [0,2 \pi] \)

Answer 1

The solutions of the equation on the interval [0, 2π] are:

Code snippet

x=pi/6

x=5pi/6

x=11pi/6

x=17pi/6

We can solve this equation as follows:

Code snippet

4cos^2(x)-3=0

cos^2(x)=3/4

cos(x)=sqrt(3)/2 or cos(x)=-sqrt(3)/2

x=pi/6+2pi*k or x=5pi/6+2pi*k, where k is any integer

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In the interval [0, 2π], the possible values of x are:

Code snippet

x=pi/6

x=5pi/6

x=11pi/6

x=17pi/6

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Therefore, the solutions of the equation on the interval [0, 2π] are:

Code snippet

x=pi/6

x=5pi/6

x=11pi/6

x=17pi/6