heughstephanie heughstephanie
  • 12-05-2024
  • Mathematics
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What is a possible value of sin θ when cos 2θ = 0.42?

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BrainLifting
BrainLifting BrainLifting
  • 12-05-2024

Answer:

sin(θ)=±0.5385

Step-by-step explanation:

We're given the following trigonometric equation:

cos(2θ)=0.42

Through the double angle formulae of Cosine, we know that:

cos(2θ)=cos²(θ)-sin²(θ)=1-2sin²(θ)

Substituting the formula in our equation:

1-2sin²(θ)=0.42

Hence,

2sin²(θ)=1-0.42

2sin²(θ)=0.58

sin²(θ)=0.29

sin(θ)=[tex]\sqrt{0.29} = \pm 0.5385[/tex]

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