Find the Value Using the Unit Circle cot(45)

Problem

cot(45^∘)

Solution

1. Identify the coordinates on the unit circle for the given angle 45^∘

2. Recall that for any point (x,y) on the unit circle, x=cos(θ) and y=sin(θ)

3. Determine the coordinates at 45^∘ which are (√(,2)/2,√(,2)/2)

4. Apply the formula for the cotangent function, which is defined as cot(θ)=cos(θ)/sin(θ) or x/y

5. Substitute the values into the formula: cot(45^∘)=√(,2)/2/√(,2)/2

6. Simplify the fraction by dividing the numerator by the denominator.

Final Answer

cot(45^∘)=1

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