![Solve the equation 2\[0.5ex] theta - 3 theta - 2 = 0 for 0^\[0.5ex] theta 360^\[0.5ex] using the t-formula.](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1778754112087-febd691da119d87b.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — here's how to solve the equation 2 - 3 - 2 = 0 for 0^ 360^ using the t-formula: Step 1: Apply the t-formula substitutions. Let t = (()/(2)). The t-formula states that = (2t)/(1+t^2) and = (1-t^2)/(1+t^2). Substitute these into the given equation: 2((1-t^2)/(1+t^2)) - 3((2t)/(1+t^2)) - 2 = 0 Step 2: Clear the denominator and simplify the equation. Multiply the entire equation by (1+t^2) to eliminate the denominators: 2(1-t^2) - 3(2t) - 2(1+t^2) = 0 Expand the terms: 2 - 2t^2 - 6t - 2 - 2t^2 = 0 Combine like terms: -4t^2 - 6t = 0 Divide by -2 to simplify: 2t^2 + 3t = 0 Step 3: Solve the quadratic equation for t. Factor out t: t(2t + 3) = 0 This gives two possible values for t: t = 0 or 2t + 3 = 0 t = -(3)/(2) Step 4: Solve for using t = (()/(2)). Case 1: t = 0 (()/(2)) = 0 The general solution for x = 0 is $x = n · 180