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.

Related questions
See all questions in Trigonometric Functions of Any Angle
Impact of this question
10152 views around the world
You can reuse this answer
Creative Commons License