Find the Value Using the Unit Circle tan(-210)

Problem

tan(−210^∘)

Solution

1. Find a coterminal angle by adding 360^∘ to the negative angle to locate its position on the unit circle.

−210^∘+360^∘=150^∘

2. Identify the coordinates for 150^∘ on the unit circle, which corresponds to the point (x,y)

(x,y)=(−√(,3)/2,1/2)

3. Apply the tangent formula using the relationship tan(θ)=y/x

tan(−210^∘)=1/2/(−√(,3)/2)

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

tan(−210^∘)=1/2⋅(−2/√(,3))

tan(−210^∘)=−1/√(,3)

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

tan(−210^∘)=−√(,3)/3

Final Answer

tan(−210^∘)=−√(,3)/3

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