Question

If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ ? (2 points)
sin Θ = square root 2 over 2 ; tan Θ = −1
sin Θ = negative square root 2 over 2 ; tan Θ = 1
sin Θ = square root 2 over 2 ; tan Θ = negative square root 2
sin Θ = negative square root 2 over 2 ; tan Θ = −1

Answer 1

Using the conditions given:
We know that θ>180°

cos θ=(√2)/2 is equivalent to cos 45° and cos 315°
45°<180° so we know it's not that.
cos 315°=(√2)/2

cos θ=2/(3π) is equivalent to cos 270°

then we plug in the degrees to sin and tan
it looks like you need sin for the first half and tan for the second, but I'm going to give you both result of sin and tan

so, sin 315°= -(√2)/2
sin 270° = -1

tan 270° = undefined
tan 315° = -1