Find all the values of theta in the interval 0 degrees less than or equal to theta less than or equal to 360 degrees that satisfy the given equation. 4sin^2(theta) + 4cos(theta) = 5

Expert Answers

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Solve `4sin^2theta+4costheta=5` on `0 <= theta <= 360`

Use the pythagorean identity:

`4(1-cos^2theta)+4costheta=5`

`4-4cos^2theta+4costheta-5=0`

`4cos^2theta-4costheta+1=0`

`(2costheta-1)^2=0`

`=>costheta=1/2`

On `0<theta<360` `costheta=1/2 => theta=60"or"300`

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Thus the solutions are `theta=60` degrees or `theta=300` degrees.

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