Please help due tonight

Question

 is in Quadrant II.

Use the given information about θ to find the exact value of tan(θ/2).

Answer 1

secx = -3

cosx = 1/secx = -1/3

sinx = (sqr(3^2 - 1^2) = (sqr9-1)/3 = sqr8/3 =(2sqr2)/3

use a half angle formula for tan(x/2)

tan(x/2) = sinx/(1+cosx) = [(sqr8)/3]/(1-1/3) = [(sqr8)/3]/(2/3) = (2sqr2/3)(3/2)=(2/3)(3/2)sqr2 = sqr2

tan(x/2) = sqr2

check the answer

sinx = sqr8/3 = about .94281

use an inverse trig function on a calculator

x =sin^-1(.94281) = 70.523 but that's quadrant I, you want quadrant II, so subtract from 180

to get 180-70.523 = 109.477 degrees

x/2 = 109.477/2 = 54.739

tan54.739 = about 1.414 = about sqr2

while x was in quadrant II, x/2 is in quadrant I so the tangent of x is positive.

Answer 2

sec θ = -3

cos θ = ? Reciprocal

tan θ/2 = ±√[(1 - cos θ) / (1 + cos θ)]