If sin ⁡x=−1/2, and 270°<x<360°, find tan⁡(x−30°).

Question

If sin ⁡x=−1/2, and 270°<x<360°, what is tan⁡(x−30°) in fractional form?

Answer 1

Hello Alice,

Since sinx = -(1/2), the given x has

cosx = (√3/2). Using the identity

tanx = (sinx/cosx/, we can work with

(sin(x - 30)/cos(x - 30))

sin(x - 30) = sinx•cos(30) - cosx•sin(30)

= (-1/2)(√3/2) - (√3/2)(1/2)

sin(x - 30) =(-2√3/4) = (-√3/2)

cos(x - 30) = cosx•cos(30) + sinx•sin(30)

= (√3/2)(√3/2) + (-1/2)(1/2)

cos(x - 30) = (1/2)

tan(x - 30) = -√3

Regards,

Anita A.