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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