Question

Use the given information to find the exact value of the expression.
sin α =21/29 , α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).
A.155/493
B.468/493
C.475/493
D.132/493

Answer 1

from your data we have:
\[\cos \alpha<0, \sin \beta>0\]
Now, we can write:
\[\cos \alpha=-\sqrt{1-(\frac{ 21 }{ 29 })^{2}}=-\frac{ 20 }{ 29 }\]
and:
\[\sin \beta=\sqrt{1-(\frac{ 15 }{ 17 })^{2}}=\frac{ 8 }{ 17 }\]
so:
\[\sin(\alpha-\beta)=\sin \alpha \cos \beta-\cos \alpha \sin \beta=\]
\[=\frac{ 21 }{ 29 }*\frac{ 15 }{ 17 }+\frac{ 20 }{ 29 }*\frac{ 8 }{ 17 }=\frac{ 475 }{ 493 }\]

Answer 2

@SkiTTleoooo47

Answer 3

Thank you!!!!!! :)

Answer 4

thank you!