Question

What is tan 11(3.14)/6

Answer 1

Answer:

A) -sqrt(3)/3

Step-by-step explanation:

If you know your unit circle (attached), 11pi/6 has the value of (sqrt(3)/2,-1/2), where the coords are (cosine, sine).

Tangent is sine/cosine:

(-1/2)/(sqrt(3)/2)

We can convert this to multiplication by miltiplying the reciprocal of sqrt(3)/2:

(-1/2)*(2/sqrt(3))

Multiplied out to:

-2/(2sqrt(3))

We have to rationalize this by multiplying the numerator and denominator by sqrt(3):

-2(sqrt(3))/2sqrt(3)(sqrt(3)

two of the same square roots multiplied together equals the number without the sqrt:

-2(sqrt(3))/2*3

we can factor out 2 from the numerator and denominator:

-sqrt(3)/3

Therefore, the answer is A