Question

Given tan A=-√5 and cos A >0, find sin A.
PLEASE HURRY AND SHOW WORK

Answer 1

sinA = -
`(√(5) )/(√(6) )`

Explanation:

Given

tanA = -
`(√(5) )/(1)` =
`(opposite)/(adjacent)`

This is a right triangle with opposite =
`√(5)`, adjacent = 1 and

hypotenuse h² = (
`√(5)` )² + 1² = 5 + 1 = 6 ⇒ h =
`√(6)`

Since tanA < 0 and cosA > 0 then A is in the 4th quadrant where sinA < 0

Then

sinA = -
`(opposite)/(hypotenuse)` = -
`(√(5) )/(√(6) )`