{"id":260562,"date":"2024-04-13T00:49:53","date_gmt":"2024-04-13T00:49:53","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=260562"},"modified":"2024-04-13T00:49:53","modified_gmt":"2024-04-13T00:49:53","slug":"how-to-find-value-of-x-which-minimizes-sinxcosx","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-to-find-value-of-x-which-minimizes-sinxcosx\/","title":{"rendered":"How to find value of x which minimizes sinxcosx?"},"content":{"rendered":"

Title: Finding the Value of x to Minimize sin(x)cos(x)<\/p>\n

Introduction:
\nIn mathematics, optimization problems often arise in various fields. One such problem involves determining the value of x that minimizes the expression sin(x)cos(x). This article will address this question directly, offering a step-by-step approach towards finding the optimal value of x.<\/p>\n

**How to find the value of x which minimizes sin(x)cos(x)?**
\nTo find the value of x that minimizes sin(x)cos(x), we can employ basic calculus techniques. Let’s begin by differentiating the given expression with respect to x.<\/p>\n

1. Differentiate the expression:
\nBy applying the product rule of differentiation, we obtain the derivative of sin(x)cos(x) as (cos^2(x) – sin^2(x)).<\/p>\n

2. Set the derivative equal to zero:
\nTo find the critical points, where the derivative equals zero, we set (cos^2(x) – sin^2(x)) = 0.<\/p>\n

3. Simplify the equation:
\nUsing the Pythagorean identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as cos^2(x) – (1 – cos^2(x)) = 0.<\/p>\n

4. Continue solving for x:
\nExpanding and rearranging the equation, we have 2cos^2(x) – 1 = 0.<\/p>\n

5. Solve for the cosine value:
\nBy isolating cos^2(x) = 1\/2, we find two possible solutions for cos(x) = \u00b1\u221a(1\/2). This yields two different angles for x: x = \u03c0\/4 and x = 3\u03c0\/4.<\/p>\n

Hence, the values of x that minimize sin(x)cos(x) are x = \u03c0\/4 and x = 3\u03c0\/4.<\/p>\n

\n
\n

Table of Contents<\/p>\nToggle<\/span><\/path><\/svg><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n