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
2 answers:
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:
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
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