Find the exact value by using a sum or difference identity. sin (200° - 80°)?

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Find the exact value by using a sum or difference identity.

sin (200° - 80°)

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Answer 1 · 2018-04-16T08:06:01

$color(blue)(sqrt(3)/2)$

Identity:

$color(red)bb(sin(A+B)=sinAcosB+cosAsinB)$

$sin(200^@-80^@)=>sin(120^@)=>sin(60^@+60^@)$

Using identity:

$sin(60^@+60^@)=sin(60)cos(60^@)+cos(60^@)sin(60^@)$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =(sqrt(3)/2)(1/2)+(1/2)(sqrt(3)/2)$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =sqrt(3)/4+sqrt(3)/4$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =(2sqrt(3))/4$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =color(blue)((sqrt(3))/2)$