Question

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

Answer 1

D

Explanation:

Using the trigonometric identities

• cscx =
`(1)/(sinx)`

• sin²x + cos²x = 1

Given

cosΘ = -
`(1)/(4)` , 180 < Θ < 270

then Θ is in the third quadrant where sinΘ < 0

sinx = -
`√(1-cos^2x)`

sinΘ = -
`√(1-(-1/4)^2)` = -
`\sqrt{(15)/(16) }` = -
`(√(15) )/(4)`

Hence

cscΘ =
`(1)/(-(√(15) )/(4) )` = -
`(4)/(√(15) )`