Find the Exact Value cos(960)

Problem

cos(960^∘)

Solution

1. Find the coterminal angle by subtracting multiples of 360^∘ until the angle is between 0^∘ and 360^∘

960^∘−2*(360^∘)=960^∘−720^∘

960^∘−720^∘=240^∘

2. Identify the quadrant for 240^∘ Since 180^∘<240^∘<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 for 240^∘ using the formula (θ_ref)=θ−180^∘

(θ_ref)=240^∘−180^∘

(θ_ref)=60^∘

5. Evaluate the cosine of the reference angle and apply the negative sign.

cos(60^∘)=1/2

cos(240^∘)=−1/2

Final Answer

cos(960^∘)=−1/2

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