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°?

2 Answers
Jun 9, 2018

#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#

Jun 9, 2018

#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!