Find the exact value of csc (theta) for an angle (theta) with cos (theta) = -2/5 and with its terminal side in Quadrant II.

a. sqrt(21)/5

b. -5/2

c. -2/5

d. 5/sqrt(21)

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Step-by-step explanation:

We are given and that 's angle terminates in quadrant 2 which means .

We will be using Pythagorean Identity: .

Since again 's angle terimates in quadrant 2, we will choose that .

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d

Step-by-step explanation:

Cosec theta = 1/sin(theta)

Cos²theta + Sin²theta = 1

Sin²theta = 1 - (-⅖)² = 21/25

Sin theta = sqrt(21)/5

Positive because Quadrant 2

Cosec theta = 5/sqrt(21)

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .