CALCULUS ONE!
posted by Sara on .
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).

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.