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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

Caroline Adams

#sin55^circ ~~0.821#

As we are aware,

#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#

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Answer 2

Emery Adkins

#sin(55˚) ~~ 0.82#

As we are aware

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

Thus,

#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#.

I hope this is useful!

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.