Find the Exact Value cot(90)

Problem

cot(90^∘)

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 θ=90^∘ into the identity.

cot(90^∘)=cos(90^∘)/sin(90^∘)

3. Determine the exact values of the cosine and sine functions at 90^∘ using the unit circle.

cos(90^∘)=0

sin(90^∘)=1

4. Simplify the fraction by substituting the known values.

cot(90^∘)=0/1

cot(90^∘)=0

Final Answer

cot(90^∘)=0

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