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
1: 2.1.1 Write down the value of . Step 1: Identify the sides relative to angle . In the right-angled triangle EFG, with E = 90^ and F = : The side opposite to is EG = 2 units. The side adjacent to is EF = 3 units. Step 2: Use the definition of tangent: = OppositeAdjacent. = (EG)/(EF) = (2)/(3) The value of is (2)/(3). 2.1.2 Write down the value of . Step 1: Identify the sides relative to angle . The side opposite to is EG = 2 units. The hypotenuse is FG = sqrt(13) units. Step 2: Use the definition of sine: = OppositeHypotenuse. = (EG)/(FG) = (2)/(sqrt(13)) Step 3: Use the definition of cosecant: = (1)/( ). = (1)/(2)sqrt(13) = sqrt(13)2 The value of is sqrt(13)2. 2.1.3 Write down the value of (90^ - ). Step 1: Recognize the relationship between angles in a right-angled triangle. Since E = 90^ and F = , the third angle G = 180^ - 90^ - = 90^ - . Step 2: Use the trigonometric identity (90^ - ) = . Step 3: From 2.1.2, we already found = (2)/(sqrt(13)). Therefore, (90^ - ) = (2)/(sqrt(13)). The value of (90^ - ) is (2)/(sqrt(13)). That's 2 down. 3 left today — send the next one.