Find the Exact Value tan(255)

Problem

tan(255)

Solution

1. Rewrite the angle as a sum of two special angles from the unit circle.

tan(255)=tan(210+45)

2. Apply the sum formula for tangent, which is tan(A+B)=(tan(A)+tan(B))/(1−tan(A)*tan(B))

tan(210+45)=(tan(210)+tan(45))/(1−tan(210)*tan(45))

3. Substitute the known values tan(210)=√(,3)/3 and tan(45)=1

(√(,3)/3+1)/(1−(√(,3)/3)*(1))

4. Simplify the complex fraction by multiplying the numerator and denominator by 3

(√(,3)+3)/(3−√(,3))

5. Rationalize the denominator by multiplying the numerator and denominator by the conjugate 3+√(,3)

((√(,3)+3)*(3+√(,3)))/((3−√(,3))*(3+√(,3)))

6. Expand the numerator and denominator.

(3√(,3)+3+9+3√(,3))/(9−3)

7. Combine like terms and simplify the fraction.

(12+6√(,3))/6

2+√(,3)

Final Answer

tan(255)=2+√(,3)

Want more problems? Check here!