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you have an angle u=120u=120 degrees. define the exact value of uu when you know that 3030 degrees =12= \frac{1}{2}

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Inverses of csc, sec, and cotright chevron icon

Full solution

Q. you have an angle u=120u=120 degrees. define the exact value of uu when you know that 3030 degrees =12= \frac{1}{2}
  1. Identify Relationship: Identify the relationship between uu and cos⁡(30°)\cos(30°).\newlineSince cos⁡(30°)=12\cos(30°) = \frac{1}{2}, we need to find cos⁡(u)\cos(u).
  2. Calculate Cosine: Calculate cos⁡(120°)\cos(120°).\newlineUsing the cosine rule for angles greater than 90°90°, cos⁡(120°)=−cos⁡(60°)\cos(120°) = -\cos(60°).
  3. Find Cosine: Find cos⁡(60°)\cos(60°). From trigonometric values, cos⁡(60°)=12\cos(60°) = \frac{1}{2}.
  4. Substitute to Find: Substitute back to find cos⁡(120°)\cos(120°).cos⁡(120°)=−12\cos(120°) = -\frac{1}{2}.

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