Find the Exact Value cos(130)

Problem

cos(130^∘)

Solution

1. Identify the given angle as 130^∘ Since this is not a standard reference angle, we look for a way to express it using standard angles or identities.

2. Apply the supplementary angle identity, which states cos(180^∘−θ)=−cos(θ)

3. Substitute 130^∘=180^∘−50^∘ into the identity.

4. Determine that cos(130^∘)=−cos(50^∘)

5. Conclude that since 50^∘ is not a standard angle (like 30^∘ 45^∘ or 60^∘, the exact value is typically left in terms of the cosine function or its cofunction. Using the cofunction identity cos(θ)=sin(90^∘−θ) we can also write this as −sin(40^∘)

Final Answer

cos(130^∘)=−cos(50^∘)

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