Find the Exact Value tan(45 degrees )

Problem

tan(45)

Solution

1. Identify the angle in the context of a unit circle or a special right triangle.

2. Recall that a 45−45−90 triangle is an isosceles right triangle where the legs are equal in length.

3. Apply the definition of the tangent function, which is the ratio of the opposite side to the adjacent side.

tan(θ)=opposite/adjacent

4. Substitute the values for a 45 angle, where the opposite and adjacent sides are both 1 (or √(,2)/2 on a unit circle).

tan(45)=1/1

5. Simplify the fraction to find the exact value.

Final Answer

tan(45)=1

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