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

D

Step-by-step explanation:

Using the trigonometric identities

• cscx =

• sin²x + cos²x = 1

Given

cosΘ = - , 180 < Θ < 270

then Θ is in the third quadrant where sinΘ < 0

sinx = -

sinΘ = - = - = -

Hence

cscΘ = = -

Shania is correct.

Step-by-step explanation:

For a right angled triangle, given two sides and an angle, we can use the sine rule or the various trigonometry identities to solve the triangle;

a/sin A = b/sinB

and

sin (angle) = opposite side/hypotenuse

cos (angle) = adjacent side/hypotenuse

tan (angle) = opposite/ adjacent

assuming a is the opposite side of angle A and b is also opposite of angle B

Otherwise, the only way to solve a triangle given two sides only is by the use of the Pythagoras theorem.

Hence, Shania is correct.