Find the exact value of tan( cos^-1 ( -5/13))

-¹²/₅  

Step-by-step explanation:

Let cos a = -⁵/₁₃

Then tan a = sin a/cos a

= [√(1 - cos²a)]/cos a

= {√[1 - (-⁵/₁₃)²]}/(-⁵/₁₃)

= -[√(1 - ²⁵/₁₆₉)] × ¹³/₅

= -[(√(¹⁴⁴/₁₆₉ )] × ¹³/₅

= -¹²/₁₃ × ¹³/₅

= -¹²/₅

tan(arccos (-⁵/₁₃)) = -¹²/₅

The diagram shows the 2nd  quadrant of a circle with radius 13, cos a = -⁵/₁₃, and tan a = ¹²/₍₋₅₎ = -¹²/₅.

answer: the answer is ann