If \( \sin(x) = \frac{3}{5} \) and \( x \) is in the first quadrant, find \( \cos(x) \).

["How to Find ( \cos(x) ) When ( \sin(x) = \frac{3}{5} ) and ( x ) Is in the First Quadrant", "If you've ever worked with trigonometric functions, you know that sine and cosine are always key players. A common problem students face is: If ( \sin(x) = \frac{3}{5} ) and ( x ) is in the first quadrant, how do I find ( \cos(x) )? The good news is it’s straightforward using the Pythagorean identity.", "### Understanding the Pythagorean Identity", "At the heart of trigonometry lies the fundamental identity:\n[\n\sin^2(x) + \cos^2(x) = 1\n]\nThis identity holds true regardless of the angle ( x ), and it connects sine and cosine through the unit circle.", "Given ( \sin(x) = \frac{3}{5} ), we first square this value:\n[\n\sin^2(x) = \left(\frac{3}{5}\right)^2 = \frac{9}{25}\n]", "### Substitute into the Identity", "Insert ( \sin^2(x) ) into the identity:\n[\n\frac{9}{25} + \cos^2(x) = 1\n]", "To isolate ( \cos^2(x) ), subtract ( \frac{9}{25} ) from both sides:\n[\n\cos^2(x) = 1 - \frac{9}{25} = \frac{25}{25} - \frac{9}{25} = \frac{16}{25}\n]", "### Solve for ( \cos(x) )", "Taking the square root of both sides gives:\n[\n\cos(x) = \pm \sqrt{\frac{16}{25}} = \pm \frac{4}{5}\n]", "But here’s the key: since ( x ) is in the first quadrant, both sine and cosine are positive in this quadrant. Therefore, we discard the negative root.", "[\n\cos(x) = \frac{4}{5}\n]", "### Conclusion", "When ( \sin(x) = \frac{3}{5} ) and ( x ) is in the first quadrant, the cosine value is:\n[\n\cos(x) = \frac{4}{5}\n]", "This method—using the Pythagorean identity—is powerful and reliable, making it essential for solving trigonometric problems efficiently.", "---", "Keywords for SEO:\nsin(x) = 3/5, find cos(x), trigonometry, first quadrant, Pythagorean identity, cos(x) calculation, mathematical tutorial, sine and cosine relationship."]