If csc theta = 8/7, which equation represents (cot theta) ?
a. cot theta=√15/8
b. cot theta=√15 / 7
c. cot theta=7√15 / 15
d. cot theta= 8√15 / 15

Out of the given choice, the equation represents .

Option B

Step-by-step explanation:

We know,

Given data:

So, now sin theta can express as

Sin theta defined by the ratio of opposite to the hypotenuse. In general, the adjacent can be calculated by,

Taking square root, we get

Also, we know the formula for cot theta,

Cos theta denoted as the ratio of adjacent to the hypotenuse.

Therefore, find now as below,

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west