Question

If `sin x = 3/5"` and `x` is acute angle, what is `cos x` and `tan x`?

Answer 1

`cosx=4/5" and "tanx=3/4`

Explanation:

`"since x is acute " 0 < x < pi/2`

`"then the trigonometric rations will be positive"`

`•color(white)(x)sin^2x+cos^2x=1`

`rArrcosx=+-sqrt(1-sin^2x)`

`color(white)(rArrcosx)=+sqrt(1-(3/5)^2)=sqrt(16/25)=4/5`

`•color(white)(x)tanx=sinx/cosx`

`rArrtanx=3/5xx5/4=3/4`

Answer 2

`cos x=4/5,tan x=3/4`

Explanation:

In the right-angled triangle:

`:.sinx=(opposite)/(hypotenuse)`

`:.cosx=(adjacent)/(hypotenuse)`

`:.tanx=(opposite)/(adjacent)`

pythagoras:

`:.3^2+a^2=5^2`

`:.a^2=5^2-3^2`

`:.a^2=25-9`

`:.a^2=16`

`:.a=sqrt16`

`:.a=4=adjacent`

`:.sin x=3/5`

`:.cosx=4/5`

`:.tanx=3/4`