Question

How do you find the exact values of `costheta` and `sintheta` when `tantheta=5/12`?

Answer 1

sinθ=`5/13`

and cosθ=`12/13`

Explanation:

Draw a right triangle with base 12 and height 5 units with angle `theta` sitting on the base as shown below

Apply Pythagoras theorem to get hypotenuse= 13 units

Work out sin`theta= 5/13`

and cos`theta= 12/13`

Answer 2

`costheta=12/13` and `sin theta=5/13`

Explanation:

If `tantheta=5/12= (opposite side)/(adjacent side)`
So the hypotenuse `=sqrt(5^2+12^2)=sqrt169=13`
`costheta=`(adjacent side)/(hypotenuse)`=12/13`
`sintheta=`(opposite side)/(hypotenuse)`=5/13`