Find the Exact Value cot(450)

Problem

cot(450^∘)

Solution

1. Identify the angle and its periodicity. The cotangent function has a period of 180^∘ meaning cot(θ)=cot(θ+180^∘*k) for any integer k

2. Subtract multiples of 180^∘ to find a coterminal angle within the standard range.

450^∘−180^∘=270^∘

270^∘−180^∘=90^∘

3. Apply the definition of the cotangent function in terms of sine and cosine.

cot(90^∘)=cos(90^∘)/sin(90^∘)

4. Substitute the known values for the trigonometric functions at 90^∘

cos(90^∘)=0

sin(90^∘)=1

5. Simplify the fraction to find the final value.

0/1=0

Final Answer

cot(450^∘)=0

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