Question

Suppose Cotangent (theta) = StartFraction 5 Over 12 EndFraction, where Pi less-than theta less-than StartFraction 3 pi Over 2 EndFraction. What is sin(θ)?
Negative StartFraction 12 Over 13 EndFraction
Negative StartFraction 5 Over 13 EndFraction
StartFraction 5 Over 13 EndFraction
StartFraction 12 Over 13 EndFraction

Answer 1

Answer:

Sin theta = 12/13

Step-by-step explanation:

From the question;

Cot theta = 5/12

Kindly recall;

Cot theta = 1/ tan theta

Hence, tan theta = 12/5

Mathematically

tan theta= opposite/adjacent

to get hypotenuse, we will use Pythagoras’ theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides

let hypotenuse be h

h^2 = 12^2 + 5^2

h^2 = 144 + 25

h^2 = 169

h = √169

h = 13

But sine theta = opposite/ hypotenuse = 12/13