`4cos^2 (x) - 4cos(x) - 1 = 0` Use the Quadratic Formula to solve the equation in the interval `0,2pi)`. Then use a graphing utility to approximate the angle `x`.

Textbook Question

Chapter 5, 5.3 - Problem 62 - Precalculus (3rd Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`4cos^2(x)-4cos(x)-1=0`

using quadratic formula,

`cos(x)=(-(-4)+-sqrt((-4)^2-4*4*(-1)))/(2*4)`

`cos(x)=(4+-sqrt(16+16))/8`

`cos(x)=(1+-sqrt(2))/2`

For cos(x)=`(1+sqrt(2))/2` , No solution since cos(x) can not be greater than one for real solutions.

Solution in the range (0,2pi) for cos(x)=

`x=arccos(1-sqrt(2))/2 , 2pi-arccos(1-sqrt(2))/2`

See attached graph

x `~~`  1.8 , 4.5

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