Finding the exact value of tan theta for an angle theta with sine theta equals 5/6 and its terminal side in quadrant 2

B

Step-by-step explanation:

Start with the definition of Tan(theta) = Sin(theta)/cos(theta)

In quad 2, cos(theta) < 0 so it is negative. That means A and C are both incorrect because both are > 0.

cos(theta) = - sqrt(1 - sin^2(theta) ) Note you have to add a minus sign here because the cosine (and tangent are both minus in quad 2).

Cos(theta) = -sqrt(1 - (5/6)^2 )

cos(theta) = -sqrt(1 - 25/36)

cos(theta) = -sqrt(11/36)

Cos(theta) = -sqrt(11)/6

Tan(theta) = sin(theta) / cos(theta)

Tan(theta) = 5/6 // - sqrt(11)/6

This is a 4 tier fraction. You invert the denominator and multiply.

Tan(theta) = 5/6 * 6/-sqrt(11)

Tan(theta) = 5 / - sqrt(11)                      

Here they rationalized the denominator

Tan(theta) = 5 sqrt(11) / (- sqrt(11)*sqrt(11) )

Tan(theta) = - 5 sqrt(11) / 11

The answer is B