Q:

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

Accepted Solution

A:
Answer:BStep-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)/6Tan(theta) = sin(theta) / cos(theta)Tan(theta) = 5/6 // - sqrt(11)/6This 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 denominatorTan(theta) = 5 sqrt(11) / (- sqrt(11)*sqrt(11) )Tan(theta) = - 5 sqrt(11) / 11 The answer is B