A point on the unit circle is given by (𝑥, 𝑦) = ( ⁄13 , ⁄13). Find sin𝜃 ,cos𝜃 ,tan𝜃.

Answer 1

While 5-12-13 is a solution it is only the unique integral solution.

The relation between x and y is not given (poorly worded problem)

Assume x = y, then x and y = 13√2 / 2 and θ = π/4 radians.

An unlimited number of non-integral solutions are possible.

Try x = y√3!

Answer 2

there is a right triangle 5-12-13

with hypotenuse 13 and sides 5 and 12

odds are you may have meant to write (5/13, 12/13) or (12/13, 5/13)

they are points on a unit circle as (5/13)^2 + (12/13)^2 = 25/169 + 144/169 = 169/169 = 1= radius

if (x,y) = (5/13, 12/13)

then

sin(theta) = 12/13

cos(theta) = 5/13

tan(theta) = 12/5

if (x,y) = (12/13, 5/13)

then

sin(theta) = 5/13

cos(theta) = 12/13

tan(theta) = 5/12