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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