Respuesta :

Answer:

tanΘ = [tex]\frac{15}{8}[/tex]

Step-by-step explanation:

Using the trigonometric identities

tan x = [tex]\frac{sinx}{cosx}[/tex]

sin²x + cos²x = 1 ⇒ sin x = ± [tex]\sqrt{1-cos^2x}[/tex]

Since 180° < Θ < 270° then sinΘ < 0 and tanΘ > 0

sinΘ = - [tex]\sqrt{1-(-8/17)^2}[/tex] = - [tex]\sqrt{1-\frac{64}{289} }[/tex] = - [tex]\sqrt{\frac{225}{289} }[/tex] = - [tex]\frac{15}{17}[/tex]

Hence

tanΘ = [tex]\frac{-\frac{15}{17} }{\frac{-8}{17} }[/tex] = - [tex]\frac{15}{17}[/tex]  × - [tex]\frac{17}{8}[/tex] = [tex]\frac{15}{8}[/tex]

Answer:

15/8.

Step-by-step explanation:

This angle is in  the third quadrant in which the  cosine is negative and the tangent is positive.

The opposite side in the triangle formed = √(17)^2 - (-8)^2)

= √(225)

= 15

So tan⁡ θ = 15/8

= 15/8.

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