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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