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Given sin A = 4/5 and cos A < 0, find tan A

User BobiYo
by
8.5k points

1 Answer

0 votes

Answer:

tan A = -
(4)/(3)

Explanation:

Using the identity sin² A + cos² A = 1, then

(
(4)/(5) )² + cos² A = 1


(16)/(25) + cos² A = 1 ( subtract
(16)/(25) from both sides )

cos² A =
(9)/(25) ( take the square root of both sides )

cos A = ±
\sqrt{(9)/(25) } and given cosA < 0, then

cos A = -
(3)/(5)

Using the identity

tan A =
(sinA)/(cosA), then

tan A =
((4)/(5) )/(-(3)/(5) ) =
(4)/(5) × -
(5)/(3) = -
(4)/(3)

User Olasimbo
by
8.3k points

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