Question

The graph of sinx and cosx intersect once between 0 and pi/2. What is the angle between the two curves at the point where they intersect? (You need to think about how the angle between two curves should be defined).

Answer 1

first find their intersection

sinx = cosx
sinx/cosx = 1
tanx = 1
x = 45° or π/4 radians

for y = sinx , dy/dx = cosx
so at x = π/4 , dy/dx = 1/√2
tan^-1(1/√2) = 35.26°

for y = cosx , dy/dx = -sinx
so at x = π/4 , dy/dx = -1/√2
tan^-1(-1/√2) = 144.74°

angle between the two tangents = 144.74 - 35.26 = 109.48°

set your calculator to radians if you need your answer in radians.