Mathematics: Given: cosθ= -4/5 , sin x = -12/13 , θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan 1/2 θanswer choices:A. -3B. 3C. 1/3

Given: cosθ= -4/5 , sin x = -12/13 , θ is in the - id4512135664476, 0prayforthelost0

Ответ:

Poohpooh6667

22.01.2022

Step-by-step explanation:

If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant. But maybe you don't know it isn't and it's a "trick" to throw you off. Hmm...

Anyways, the half angle identity for tangent is

$tan(\frac{\theta}{2})=\frac{sin\theta}{1+cos\theta}$

There are actually 3 identities for the tangent of a half angle, but this one works just as well as either of the others do, so I'm going with this one.

If theta is in QIII, the value of -4 goes along the x axis and the hypotenuse is 5. That makes the missing side, by Pythagorean's Theorem, -3. Filling in our formula:

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{1+(-\frac{4}{5}) }$ which simplifies a bit to