Doug C. answered • 02/01/18

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Hi Michael,

Think of the reference angle and associated triangle for angle B. Its opposite side will be -1 with a hypotenuse of 3. Use Pythagorean theorem to get adjacent side: 2√2 (which will be negative in QIII). This means the cos B = -2√2/3.

There are several different formulas for the tan B/2, one of them is (1-cos B)/sin B.

Substituting what we know: (1 - (-2√2/3))/-1/3 gives (1+2√2/3)/-1/3. This is a complex fraction which I would simplify by multiplying both numerator and denominator of the "big" fraction by 3.

(3+2√2)/-1 = -3-2√2

That is just one possible form for the answer. If you use tan B/2 = √(1-cosB)/(1+cosB) your answer would look different, but it would evaluate to the same value.