How do you use the angle sum identity to find the exact value of sin 195?

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Answer 1 · 2015-05-21T14:15:44

sin 195 = sin (15 + 180) = - sin 15 = -sin (pi)/12 = -.0.26

Answer 2 · 2015-05-21T17:35:50

Find two angles whose sine and cosine you know and that add up to $195^@$

$15 + 180$ will work, if you know $sin 15$

$30 +165$ -- I don't recognize $165^@$ as a multiple of a special angle.

$45 + 150$ -- I note that 150 is divisible by 30, so I should know the sine and cosine of $150^@$

$150^@ = 5xx30^@$ and $sin150^@ = 1/2$ and $cos150^@ = -sqrt3/2$

So
$sin195^@ = sin(45^@+150^@) = sin45^@ cos150^@ + cos45^@ sin150^@$

$= (sqrt2 /2) ((-sqrt3)/2) + (sqrt2/2)(1/2)$

$= (-sqrt2 sqrt3)/4 + sqrt2/4 = (-sqrt6)/4 + sqrt2/4$

$=(sqrt2-sqrt6)/4$