If sin 0= 15/17, then:?

sinθ = 15/17

As sinθ = (opposite side) / hypotenuse
Consider angle θ in a right-angled triangle, where the opposite side is 15 and the hypotenuse is 17.

By Pythagorean theorem :
adjacent side = √(17² - 15²) = √64 = 8

cosθ = (adjacent side) / hypotenuse
Then, cosθ = 8/17

secθ = 1/cosθ
Then, secθ = 17/8

tanθ = (opposite side) / (adjacent side)
Then, tanθ = 15/8

cscθ = 1/sinθ
Then, cscθ = 17/15

cotθ = 1/tanθ
Then, cotθ = 8/15

sin0 = 0, not 15/17

If sin θ = 15/17, then sec Ө = 17/8

sin Ө = 15/17
cos Ө = 8/17
tan Ө = 15/8
csc Ө = 17/15
sec Ө = 17/8
cot Ө = 8/15