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Find the value of csc theta ; if cos theta= -1/4 ; 180° < theta < 270°.


can y'all explain your answer for me lol

A.) 4/-15

B.) 4/√15

C.) -4

D.) -4/√15

Respuesta :

Answer:

D

Step-by-step explanation:

Using the trigonometric identities

• cscx = [tex]\frac{1}{sinx}[/tex]

• sin²x + cos²x = 1

Given

cosΘ = - [tex]\frac{1}{4}[/tex] , 180 < Θ < 270

then Θ is in the third quadrant where sinΘ < 0

sinx = - [tex]\sqrt{1-cos^2x}[/tex]

sinΘ = - [tex]\sqrt{1-(-1/4)^2}[/tex] = - [tex]\sqrt{\frac{15}{16} }[/tex] = -[tex]\frac{\sqrt{15} }{4}[/tex]

Hence

cscΘ = [tex]\frac{1}{-\frac{\sqrt{15} }{4} }[/tex] = - [tex]\frac{4}{\sqrt{15} }[/tex]

Answer:

D. -(4/sqrt15)

Step-by-step explanation:

edg2021

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