Algebraically show that f(x) = sin(x) and g(x) = cos(x) intersect at x = π/4

thanks

Substitute π/4 at both functions.

sin (π/4) = √(2)/2

cos (π/4) = √(2)/2

Since the resulting values are equal, then the two functions intersect at x = π/4.

f(x) and g(x) will intersect at a point which satisfies both functions ie., f(x) = g(x)

=> sin(x) = cos(x)

=> tan(x) = 1

=> x = π/4

Use a trigonometric identity to show the point of intersection:
sinx = cosx
sinx = sin(π / 2 - x)
x = π / 2 - x
2x = π / 2
x = π / 4

sin(x)=cos(x)
tan(x)=1
basic angle=(pi)/4

yes. sinpi/4=cospi/4=1/root2