Evaluate tan(30 degrees )

Problem

tan(30)

Solution

1. Identify the angle in the context of the unit circle or a special right triangle. The angle 30 corresponds to the radian measure π/6

2. Recall the definition of the tangent function in terms of sine and cosine.

tan(θ)=sin(θ)/cos(θ)

3. Substitute the known values for sin(30) and cos(30)

sin(30)=1/2

cos(30)=√(,3)/2

4. Calculate the ratio by dividing the two values.

tan(30)=1/2/√(,3)/2

5. Simplify the fraction by multiplying by the reciprocal of the denominator.

tan(30)=1/√(,3)

6. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

tan(30)=√(,3)/3

Final Answer

tan(30)=√(,3)/3

Want more problems? Check here!