How do you use the reference angles to find #sin210cos330-tan 135#?

1 Answer
Zor Shekhtman
Feb 3, 2015

#sin(210)=sin(180+30)=-sin(30)=-1/2#
#cos(330)=cos(360-30)=cos(-30)=cos(30)=sqrt(3)/2#
#tan(135)=sin(180-45)/cos(180-45)=sin(45)/-cos(45)=(sqrt(2)/2)/(-sqrt(2)/2)=-1#
The answer, therefore, is
#(-1/2)*(sqrt(3)/2)-(-1)=1-sqrt(3)/4=0.567# (approximately)

The simple trigonometric identities used in the above calculations are:
#sin(x+π) = −sin(x)#
#sin(x−π) = −sin(x)#
#sin(π−x) = sin(x)#
#cos(x+π) = −cos(x)#
#cos(x−π) = −cos(x)#
#cos(π−x) = −cos(x)#
These any many other useful properties of trigonometric functions are explained in details in the chapter on Trigonometry on a Web site Unizor - a free Web site dedicated to advanced math for high school students.

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