Question

If the cos θ = 5/13 and tan θ = 12/5, what is sin θ?

Answer 1

`(12)/(13)`

Explanation:

Using the trigonometric identity

tan x =
`(sinx)/(cosx)` ( multiply both sides by cos x )

sin x = tan x × cos x, that is

sinΘ = tanΘ × cosΘ

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

Answer 2

Answer: 12/13....Remember the shortcut SOH CAH TOA ——> sin = opposite/hypotenuse, cos = adjacent/hypotenuse, and tan = opposite/adjacent...know that for this problem tells you that cos = 5/13 and tan = 12/5 so thus sin = 12/13 (opposite = numerator of tan, hypotenuse = denominator of cos)