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θ\theta is an acute angle. Find the value of θ\theta in degrees.\newlinesec⁡(θ)=2\sec(\theta) = \sqrt{2}\newlineθ=\theta = ____°\degree

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Inverses of csc, sec, and cotright chevron icon

Full solution

Q. θ\theta is an acute angle. Find the value of θ\theta in degrees.\newlinesec⁡(θ)=2\sec(\theta) = \sqrt{2}\newlineθ=\theta = ____°\degree
  1. Secant and Cosine Relationship: sec⁡(θ)\sec(\theta) is the reciprocal of cos⁡(θ)\cos(\theta), so if sec⁡(θ)=2\sec(\theta) = \sqrt{2}, then cos⁡(θ)=12\cos(\theta) = \frac{1}{\sqrt{2}}.
  2. Secant Value Calculation: But wait, we know that cos⁡(45°)=2/2\cos(45°) = \sqrt{2}/2, which is the same as 1/21/\sqrt{2} if we rationalize the denominator.

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