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#