Question

If tan tan x degrees equals a over 4 and cos x degrees equals 4 over b, what is the value of sin x°?

Answer 1

Given:

`\begin{gathered} tan\text{ x = }(a)/(4) \\ cos\text{ x= }(4)/(b) \end{gathered}`

Recall that for a right-angled triangle, the following trigonometric ratios are defined

`\begin{gathered} sin\text{ }\theta\text{ = }(opposite)/(hypothenuse) \\ cos\text{ }\theta\text{ = }(adjacent)/(hypothenuse) \\ tan\theta\text{ = }(opposite)/(adjacent) \end{gathered}`

From the given ratios, we have:

opposite = a

adjacent = 4

hypothenuse = b

Hence, the value of sin x :

`sin\text{ x = }(a)/(b)`

Answer:

`sin\text{ x = }(a)/(b)\text{ \lparen Option C\rparen}`