Find the Exact Value tan(30 degrees )

Problem

tan(30^∘)

Solution

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

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 the sine and cosine of 30^∘

sin(30^∘)=1/2

cos(30^∘)=√(,3)/2

4. Calculate the ratio by dividing the two fractions.

tan(30^∘)=1/2/√(,3)/2

5. Simplify the expression by canceling the common denominator of 2

tan(30^∘)=1/√(,3)

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

tan(30^∘)=(1⋅√(,3))/(√(,3)⋅√(,3))

tan(30^∘)=√(,3)/3

Final Answer

tan(30^∘)=√(,3)/3

Want more problems? Check here!