Si \(\sin \theta = \frac{3}{5}\) et \(\theta\) est dans le premier quadrant, trouver \(\cos \theta\).
["Title: Find (\cos \ heta) When (\sin \ heta = \frac{3}{5}) in the First Quadrant – Step-by-Step Guide", "In trigonometry, one of the most fundamental relationships is the Pythagorean identity:", "[\n\sin^2 \ heta + \cos^2 \ heta = 1\n]", "Given that (\sin \ heta = \frac{3}{5}) and (\ heta) lies in the first quadrant, we know both sine and cosine are positive. Our goal is to find (\cos \ heta).", "### Step 1: Plug (\sin \ heta) into the identity\nStart by squaring the given sine value:", "[\n\sin^2 \ heta = \left( \frac{3}{5} \right)^2 = \frac{9}{25}\n]", "Now substitute into the Pythagorean identity:", "[\n\frac{9}{25} + \cos^2 \ heta = 1\n]", "### Step 2: Solve for (\cos^2 \ heta)", "[\n\cos^2 \ heta = 1 - \frac{9}{25} = \frac{25}{25} - \frac{9}{25} = \frac{16}{25}\n]", "### Step 3: Take the square root", "[\n\cos \ heta = \sqrt{\frac{16}{25}} = \frac{4}{5}\n]", "Since (\ heta) is in the first quadrant, (\cos \ heta) is positive. Therefore,", "[\n\cos \ heta = \frac{4}{5}\n]", "---", "### Summary", "Given (\sin \ heta = \frac{3}{5}) and (\ heta) in the first quadrant:\n- Use the identity (\sin^2 \ heta + \cos^2 \ heta = 1)\n- Solve algebraically for (\cos \ heta)\n- Take the positive root due to quadrant constraints", "[\n\boxed{\cos \ heta = \frac{4}{5}}\n]", "This method ensures accuracy and clarity when solving inverse trigonometric problems, especially in competitive exams or real-world applications requiring precise angular measurements.", "---", "Keywords: (\sin \ heta = \frac{3}{5}), (\cos \ heta), first quadrant trigonometry, Pythagorean identity, inverse trig functions, solve cosine, angular relationships", "Meta description: Find (\cos \ heta) when (\sin \ heta = \frac{3}{5}) and (\ heta) is in the first quadrant using the Pythagorean identity (\sin^2 \ heta + \cos^2 \ heta = 1). Step-by-step solution explained."]
