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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