antlopezpd74nm
contestada

Use a sum or difference formula to find the exact value of the following.
[tex] sin\frac{13\pi}{28}cos\frac{2\pi}{7}+cos\frac{13\pi}{28}sin\frac{2\pi}{7} [/tex]

Respuesta :

You can see that your expression is in the form

[tex] \sin(a)\cos(b) + \cos(a)\sin(b) [/tex]

By the sine sum formula, this is the same as [tex] \sin(a+b) [/tex]

Since in your case

[tex]a = \cfrac{13\pi}{28},\quad b = \cfrac{2\pi}{7} [/tex]

your expression evaluates to

[tex] \sin\left(\cfrac{13\pi}{28} + \cfrac{2\pi}{7}\right) = \sin\left(\cfrac{3\pi}{4} \right) = \cfrac{1}{\sqrt{2}} = \cfrac{\sqrt{2}}{2} [/tex]

bawbdmo

[tex] \sin{x}\cos{y}+\cos{x}\sin{y}=\sin{x+y} \implies \\
\sin(x+y)=\sin{\frac{13\pi}{28}+\frac{2\pi}{7}} \implies \\
\sin(x+y)=\sin{\frac{13\pi}{28}+\frac{8\pi}{28}}\implies \\
\sin(x+y)=\sin{\frac{21\pi}{28}} \implies \\
\sin(x+y)=\sin{\frac{3\pi}{4}}=\frac{\sqrt{2}}{2} [/tex]

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