Final answer:
To find the equation of the tangent line to the curve y = sin(x) * cos(x) at x = π/4, we need to find the derivative of the curve and evaluate it at x = π/4. The derivative of y with respect to x is given by dy/dx = cos^2(x) - sin^2(x). Evaluating this derivative at x = π/4 gives dy/dx = cos^2(π/4) - sin^2(π/4) = 1/2 - 1/2 = 0. Therefore, the slope of the tangent line is 0. Since the slope of the tangent line is 0, the equation of the tangent line is a horizontal line passing through the point (x, y), where x = π/4 and y = sin(π/4) * cos(π/4) = 1/2 * 1/2 = 1/4. Therefore, the equation of the tangent line is y = 1/4.
Step-by-step explanation:
To find the equation of the tangent line to the curve y = sin(x) * cos(x) at x = π/4, we need to find the derivative of the curve and evaluate it at x = π/4. The derivative of y with respect to x is given by dy/dx = cos^2(x) - sin^2(x). Evaluating this derivative at x = π/4 gives dy/dx = cos^2(π/4) - sin^2(π/4) = 1/2 - 1/2 = 0. Therefore, the slope of the tangent line is 0.
Since the slope of the tangent line is 0, the equation of the tangent line is a horizontal line passing through the point (x, y), where x = π/4 and y = sin(π/4) * cos(π/4) = 1/2 * 1/2 = 1/4. Therefore, the equation of the tangent line is y = 1/4.