Question

Given sin 40° ≈ 0.64, cos 40° ≈ 0.77, sin 15° ≈ 0.26, and cos 15° ≈ 0.97, which expression could be used to estimate sin 55°?

Answer 1

`sin55^circ ~~0.821`

Explanation:

We know that,

`color(blue)(sin(A+B)=sinAcosB+cosAsinB`

Take, `A=40^circ ,B=15^circ`

#sin(40^circ+15^circ)=sin40^circcos15^circ+cos40^circsin15^circ #

`sin(55^circ)~~(0.64)(0.97)+(0.77)(0.26)`

`sin 55^circ~~0.6208+0.2002`

`sin55^circ ~~0.821`

Answer 2

`sin(55˚) ~~ 0.82`

Explanation:

We know that

`sin(a + b) = sinacosb + sinbcosa`

Therefore

`sin(40˚ + 15˚) = sin40˚cos15˚ + sin15˚cos40˚`
`sin(40˚+ 15˚) = 0.64(0.97) + 0.26(0.77)`
`sin(55˚) = 0.82`

And if we use a calculator to estimate `sin(55˚)`, we see that it does have a value of approximately `0.82`.

Hopefully this helps!