Find the Exact Value cos(570)

Problem

cos(570^∘)

Solution

1. Find the coterminal angle by subtracting 360^∘ from the given angle to bring it within the standard 0^∘ to 360^∘ range.

570^∘−360^∘=210^∘

2. Identify the quadrant for 210^∘ Since 180^∘<210^∘<270^∘ the angle lies in Quadrant III.

3. Determine the sign of the cosine function in Quadrant III. In this quadrant, cosine is negative.

4. Calculate the reference angle by subtracting 180^∘ from the angle.

(θ_ref)=210^∘−180^∘=30^∘

5. Evaluate the cosine of the reference angle using known trigonometric values.

cos(30^∘)=√(,3)/2

6. Apply the sign from step 3 to the result from step 5.

cos(210^∘)=−√(,3)/2

Final Answer

cos(570^∘)=−√(,3)/2

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