Question

If tan x° = 11 divided by r and cos x° = r divided by s, what is the value of sin x°?

Answer 1

`\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent}\\\\ -------------------------------\\\\ tan(x^o)=\cfrac{11}{r}\cfrac{\leftarrow opp}{\leftarrow adj}\qquad cos(x^o)=\cfrac{r}{s}\cfrac{\leftarrow adj}{\leftarrow hyp}\\\\\\ \boxed{sin(x^o)=\cfrac{11}{s}\cfrac{\leftarrow opp}{\leftarrow hyp}}`

Answer 2

`sin x = (11)/(s)`

Explanation:

`Tan x = (11)/(r)`

`Cos x = (r)/(s)`

Property :
`(sin \theta)/(cos \theta)=Tan \theta`

So,
`(sinx)/(cosx)=Tan x`

Substitute the values

`(sinx)/( (r)/(s))=(11)/(r)`

`sinx =(11)/(r) * (r)/(s)`

`sinx =(11)/(s)`

Hence the value of sin x° is
`(11)/(s)`