gregoryyoung48959 gregoryyoung48959
  • 12-08-2021
  • Mathematics
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12) Find the angles between 0o and 360o where sec θ = −3.8637 . Round to the nearest 10th of a degree:

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sqdancefan
sqdancefan sqdancefan
  • 20-08-2021

9514 1404 393

Answer:

  105.0°, 255.0°

Step-by-step explanation:

Many calculators do not have a secant function, so the cosine relation must be used.

  sec(θ) = -3.8637

  1/cos(θ) = -3.8637

  cos(θ) = -1/3.8637

  θ = arccos(-1/3.8637) ≈ 105.000013°

The secant and cosine functions are symmetrical about the line θ = 180°, so the other solution in the desired range is ...

  θ = 360° -105.0° = 255.0°

The angles of interest are θ = 105.0° and θ = 255.0°.

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