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
Hey Boaz, good to see you again. Here are the solutions for the given trigonometric expressions: a) Find Step 1: Use the identity ^2 + ^2 = 1. Given = (1)/(4). ^2 + ((1)/(4))^2 = 1 ^2 + (1)/(16) = 1 ^2 = 1 - (1)/(16) ^2 = (16)/(16) - (1)/(16) ^2 = (15)/(16) Since is acute, is positive. = sqrt((15)/(16)) = sqrt(15)4 b) Find ^2 Step 2: Use the identity ^2 = (^2 )/(^2 ). From Step 1, we have ^2 = (15)/(16). We are given = (1)/(4), so ^2 = ((1)/(4))^2 = (1)/(16). ^2 = (15)/(16)(1)/(16) ^2 = (15)/(16) × (16)/(1) ^2 = 15 c) Find (1)/(^2 ) Step 3: Use the value of ^2 from Step 1. We found ^2 = (15)/(16). (1)/(^2 ) = (1)/(15)16 (1)/(^2 ) = (16)/(15) Drop the next question! 📸