Find the Exact Value cot(45)

Problem

cot(45^∘)

Solution

1. Identify the trigonometric identity for the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Substitute the given angle of 45^∘ into the identity.

cot(45^∘)=cos(45^∘)/sin(45^∘)

3. Recall the exact values for sin(45^∘) and cos(45^∘) from the unit circle.

sin(45^∘)=√(,2)/2

cos(45^∘)=√(,2)/2

4. Simplify the expression by dividing the two equal values.

cot(45^∘)=√(,2)/2/√(,2)/2

cot(45^∘)=1

Final Answer

cot(45^∘)=1

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