What is the angle between sinn pi x and sinm pi x for positi

What is the angle between sin(n pi x) and sin(m pi x) for positive integers n and m? Use the inner product defined in problem 4. Optional: For each norm ||middot||_1, ||middot||_2, ||middot||_infinity, draw the set of all unit vectors in R^2. Please label your drawing. Optional: For each norm ||middot||_1, ||middot||_2, ||middot||_infinity, draw the set of all unit vectors in R^3. Please label your drawing.

Solution

Solution : 7

Angle = ( tan ^{- (m cos(mx)} - tan ^{- (n cos(nx)}) / [1+ (tan ^{- (m cos(mx)})(tan ^{- 1(n cos(nx)}]