Question 724700: Write the expression as the sine, cosine, and tangent of an angle:
Sin 330 cos 45 - cos 330 sin 45
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write the expression as the sine, cosine, and tangent of an angle:
Sin 330 cos 45 - cos 330 sin 45
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Use sin addition formula: sin(s-t)=sin s cos t-cos s sin t
Sin 330 cos 45 - cos 330 sin 45=sin(330-45)=sin(285)
reference angle=360-285=75º(in quadrant IV where sin<0), cos>0, tan<0
sin75º=sin(30+45)
=sin 30 cos 45-cos 30 sin 45
=1/2*√2/2-√3/2*√2/2
=√2/4-√6/4
=(√2-√6)/4
sin 75=-(√2-√6)/4
...
cos75º=cos(30+45)
=cos 30 cos 45-sin 30 sin 45
=√3/2*√2/2-1/2*√2/2
=√6/4-√2/4
=(√6-√2)/4
cos 75º=(√6-√2)/4
..
tan75º=tan(30+45)
=(tan 30+tan 45)/tan 30*tan 45
=(√3/3+1)/√3/3*1
=(√3/3+1)/√3/3
tan75º=-(√3/3+1)/√3/3
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