Find the Exact Value cos(450)

Problem

cos(450^∘)

Solution

1. Identify the angle and determine if it is within the standard range of 0^∘ to 360^∘ Since 450^∘ is greater than 360^∘ we must find a coterminal angle.

2. Subtract multiples of 360^∘ to find the coterminal angle.

450^∘−360^∘=90^∘

3. Evaluate the cosine function at the coterminal angle. The value of cos(450^∘) is equivalent to the value of cos(90^∘)

cos(450^∘)=cos(90^∘)

4. Determine the exact value using the unit circle. At 90^∘ the coordinates are (0,1) Since cos(θ) corresponds to the xcoordinate:

cos(90^∘)=0

Final Answer

cos(450^∘)=0

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