Question

Find the value of tan theta if sin theta = 12/13 and theta is in quadrant 2

Answer 1

tanΘ = -
`(12)/(5)`

Explanation:

Using the trigonometric identities

• sin²x + cos²x = 1, hence

cosx = ± √(1 - sin²x )

• tanx =
`(sinx)/(cosx)`

given sinΘ =
`(12)/(13)`, then

cosΘ = ±
`√(1-(12/13)^2)`

Since Θ is in the second quadrant where cosΘ < 0, then

cosΘ = -
`\sqrt{1-(144)/(169) }`

= -
`\sqrt{(25)/(169) }` = -
`(5)/(13)`

tanΘ =
`((12)/(13) )/((-5)/(13) )`

=
`(12)/(13)` × -
`(13)/(5)` = -
`(12)/(5)`