Question

Help with trigonometry​

Answer 1

○B.
`(√(6))/(2)`

Explanation:

Trigonometric Identities

`(y)/(r) = sin\:θ`

`(x)/(r) = cos\:θ`

`(y)/(x) = tan\:θ`

`(r)/(x) = sec\:θ`

`(r)/(y) = csc\:θ`

`(x)/(y) = cot\:θ`

Radius Formula

`{y}^(2) + {x}^(2) = {r}^(2)`

`{[-√(15)]}^(2) + {[-√(10)]}^(2) = {r}^(2) → 15 + 10 = {r}^(2) → 25 = {r}^(2)\\ \\ 5 = r`

* Since we are talking about radii, we only want the NON-NEGATIVE root.

In this case, we will not be using the radius in our ratio, according to the trigonometric identity above because we are using the tangent ratio:

`(√(6))/(2) = (-√(15))/(-√(10)) = \sqrt{1(1)/(2)}`

I am joyous to assist you anytime.