# 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°?

Jun 9, 2018

$\sin {55}^{\circ} \approx 0.821$

#### 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

$\sin \left({55}^{\circ}\right) \approx \left(0.64\right) \left(0.97\right) + \left(0.77\right) \left(0.26\right)$

$\sin {55}^{\circ} \approx 0.6208 + 0.2002$

$\sin {55}^{\circ} \approx 0.821$

Jun 9, 2018

sin(55˚) ~~ 0.82

#### Explanation:

We know that

$\sin \left(a + b\right) = \sin a \cos b + \sin b \cos a$

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!