Question

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

Answer 1

`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.