Question

If sin Θ = negative square root 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ? cos Θ = negative 1 over 2; tan Θ = square root 3 cos Θ = negative 1 over 2; tan Θ = −1 cos Θ = square root 3 over 4; tan Θ = −2 cos Θ = 1 over 2; tan Θ = square root 3

Answer 1

Answer:

The correct option is the option with:

cos Θ = 1/2

tan Θ = -√3

Step-by-step explanation:

Given that

sin Θ = -√3/2

We want to find the values of

cos Θ and tan Θ

First of all,

arcsin (-60) = -√3/2

=> Θ = 60

tan Θ = (sin Θ)/(cos Θ)

tan Θ = (-√3/2)/(cos Θ)

cos Θ tan Θ = (1/2)(-√3)

Knowing that Θ = -60,

and cos Θ = cos(-Θ), comparing the last equation, we have

cos Θ = 1/2

tan Θ = -√3

Answer 2

Answer:

cos Θ = 1 over 2; tan Θ = negative square root 3

Step-by-step explanation:

Given:

Sin θ = -√3/2

From trigonometry identity,

Sin^2 θ + cos^2 θ = 1

Cos θ = √(1 - sin^2 θ )

= √(1 - (-√3/2)^2)

= √(1 - (3/4))

= √(1/4)

= 1/2

Also from trigonometry,

Sin θ/cos θ = tan θ

tan θ = (-√3/2)/(1/2)

= -√3