anonymous
  • anonymous
f(θ) = (3cosθ−sinθ)^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
simplify the espression
Mertsj
  • Mertsj
\[(3\cos \theta-\sin \theta)^2=9\cos ^2\theta-6\sin \theta \cos \theta+\sin ^2\theta\]
Mertsj
  • Mertsj
Remember that sin^2(x) + cos^2(x)=1

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anonymous
  • anonymous
1. f(θ) = 5−3sin2θ+4cos2θ 2. f(θ) = 4−3sin2θ+5cos2θ 3. f(θ) =−3+5sin2θ+4cos2θ 4. f(θ) = 4+4sin2θ−3cos2θ 5. f (θ) = 5+4sin2θ−3cos2θ 6. f(θ) = 3+4sin2θ+5cos2θ
anonymous
  • anonymous
its one of those answers
anonymous
  • anonymous
but idk which
anonymous
  • anonymous
6sinθcosθ = 3sin2θ - thats one bit of it done
Mertsj
  • Mertsj
1st one
anonymous
  • anonymous
ahh yes 8 cos^2 θ + cos^2θ + sin^2θ = 8cos^2θ + 1 and 8 cos^2 θ = 4cos2θ + 4 combine to give 1st one
Mertsj
  • Mertsj
\[9\cos^2\theta=9(1-\sin^2\theta)=9-9\sin^2\theta\] Now add the sin^2 theta \[9-9\sin^2\theta+\sin^2\theta=9+8\sin^2\theta\]
Mertsj
  • Mertsj
But \[\sin^2\theta=\frac{1-\cos2\theta}{2}\]
Mertsj
  • Mertsj
Whoops. Sign error 9-8sin^2 theta
anonymous
  • anonymous
yup - very nice

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