Find the Value Using the Unit Circle tan(45)

Problem

tan(45)

Solution

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

2. Recall that at 45 (or π/4 radians), the coordinates (x,y) are (√(,2)/2,√(,2)/2)

3. Apply the formula for the tangent function in terms of the unit circle coordinates, which is tan(θ)=y/x

4. Substitute the values into the formula:

tan(45)=√(,2)/2/√(,2)/2

5. Simplify the expression by dividing the numerator by the denominator. Since they are identical and non-zero, the result is 1

Final Answer

tan(45)=1

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