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Find cos theta, where theta is the angle shown. Give an exact value, not a decimal approximation.

Find cos⁡θ \cos \theta , where θ \theta is the angle shown.\newlineGive an exact value, not a decimal approximation.

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Full solution

Q. Find cos⁡θ \cos \theta , where θ \theta is the angle shown.\newlineGive an exact value, not a decimal approximation.
  1. Identify sides for θ\theta: Identify the sides of the right triangle associated with θ\theta.
  2. Use cosine definition: Use the definition of cosine, which is cos⁡(θ)=adjacenthypotenuse\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}.
  3. Read side lengths: Read the lengths of the adjacent side and the hypotenuse from the triangle.
  4. Calculate cos⁡(θ)\cos(\theta): Calculate cos⁡(θ)\cos(\theta) using the lengths of the sides.

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