Respuesta :

Answer:

B. [tex]\frac{\sqrt{6}}{2}[/tex]

Step-by-step explanation:

Trigonometric Identities

[tex]\frac{y}{r} = sin\:θ[/tex]

[tex]\frac{x}{r} = cos\:θ[/tex]

[tex]\frac{y}{x} = tan\:θ[/tex]

[tex]\frac{r}{x} = sec\:θ[/tex]

[tex]\frac{r}{y} = csc\:θ[/tex]

[tex]\frac{x}{y} = cot\:θ[/tex]

Radius Formula

[tex]{y}^{2} + {x}^{2} = {r}^{2}[/tex]

[tex]{[-\sqrt{15}]}^{2} + {[-\sqrt{10}]}^{2} = {r}^{2} → 15 + 10 = {r}^{2} → 25 = {r}^{2}\\ \\ 5 = r[/tex]

* 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:

[tex]\frac{\sqrt{6}}{2} = \frac{-\sqrt{15}}{-\sqrt{10}} = \sqrt{1\frac{1}{2}}[/tex]

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