Question

How to find different values of Sin; Cos; Tan θ other than 0 , 30 , 45 , 60 , 90. Tell me all the ways possible plz.

Answer 1

For example lets find the value of Sin 75.

Sin 75 we can write it as.

Sin (45+30)

We need to know.

1. Sin(x+y) = sinx. cosy + cosx. siny
2. sin(x-y) = sinx.cosy - cosx. siny
3. Cos(x+y) = cosx. cosy - sinx. siny
4. Cos(x-y) = cosx. cosy + sinx. siny.

For, Sin (45+30) compare with Sin(x+y)

Sin(45+30) =( Sin45 × cos 30) + (cos 45 × sin30)

= (1/root2 × Root 3/2) + (1/root2 × 1/2)

= 1+root 3 / 2×root 2.

This is the answer here. like that you can do for other values.