Question

If sin theta = 3/5 and theta is acute, how do you calculate cos theta and tan theta?

Answer 1

`costheta=4/5`
`tantheta=3/4`

Explanation:

`sintheta=3/5`
`costheta=sqrt(1-sin^2theta`
or
`costheta=sqrt(1-(3/5)^2)`
or
`costheta=sqrt(1-9/25`
or
`costheta=sqrt((25-9)/25)`
or
`costheta=sqrt(16/25)`
or
`costheta=4/5`------------Ans `1`

`tantheta=sintheta/costheta`
or
`tantheta=(3/5)/(4/5)`
or
`tantheta=3/4`-------------Ans `2`

Answer 2

`costheta=4/5, and, tantheta=3/4`.

Explanation:

We will use the Identity `: sin^2theta+cos^2theta=1`.

`:. cos^2theta=1-sin^2theta=1-(3/5)^2=1-9/25=16/25`

`:. costheta=sqrt(16/25)=+-4/5`

But we know that theta is acute , so, it is in the first quadrant, in which, all the Trgo. ratios are `+ve`

Hence, `costheta=+4/5`.

Finally, `tantheta=sintheta/costheta`..............[Defn.]

`=(3/5)/(4/5)=3/4`