Find the cosine of ∠X.
Write your answer in simplified, rationalized form. Do not round.

The terminal side of an angle θ in standard position intersects the unit circle at (12/13 , 5/13). What is sin(θ)? Write your answer in simplified, rationalized form.

SinѲ = 5/13

Step-by-step explanation:

We have radius (r) and angle (Ѳ) theta.

Where, x, y :

x = r cosѲ ….Equation 1

and y = r sinѲ Equation 2

r = √x² + y²

In the question we are given points on the unit circle as (12/13 , 5/13)

Where x = 12/13 , y = 5/13

r = √(12/13)² + (5/13)²

r = √144/169 +25/169

r = √169/169

r = √1

r = 1

In the question, we are asked to find sinѲ. Using Equation 2,

y = r sinѲ

Where y = 5/13 and r = 1

5/13 = 1 sinѲ

Divide both sides by 1

sinѲ = 5/13

Therefore, sinѲ = 5/13