Question 723889: Find all values of θ, to the nearest degree, that satisfy the equation 7cos cubedθ = 5cos squaredθ +cosθ in the interval 0< θ < 360
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find all values of θ, to the nearest degree, that satisfy the equation 7cos cubedθ = 5cos squaredθ +cosθ in the interval 0< θ < 360
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7cos^3x=5cos^2x+cosx
7cos^3x-5cos^2x-cosx=0
cosx(7cos^2x-5cosx-1)=0
cosx=0
x=90º,270º
..
7cos^2x-5cosx-1)=0
solve for cos x by quadratic formula:
cosx≈-0.1629
using inverse cos key on calculator:
x≈99º, 261º( in quadrants II and III where cos<0)
or
cosx≈0.8772
using inverse cos key on calculator:
x≈28.7º, 331º( in quadrants I and IV where cos>0)
..
all values of θ in the interval 0< θ < 360: 90º, 270º, 99º, 261º, 28.7º, 331º
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