Question

How do you evaluate trig functions without a calculator

Answer 1

You can't in theory. Only a few "nice" values are known, because they lead to particular triangles. For example, we have

• 
  `\sin(0)=0,\quad \cos(0)=1`
• 
  `\sin(30)=(1)/(2),\quad \cos(30)=(√(3))/(2)`
• 
  `\sin(45)=\cos(45)=(√(2))/(2)`

You can add other angles using symmetries, for example, you can compute sin(60) using sin(90-x) = cos(x), or similar stuff.

You can also use the double/half angles identities to add another couple of angles in our list, but that's it.