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 Until — ready when you are. Step 1: Determine the values of x, y, and r. Given = (12)/(-5) and 90^ 180^. Since = (y)/(x), we have y = 12 and x = -5. The angle is in the second quadrant, which is consistent with x being negative and y being positive. Now, calculate the hypotenuse r using the Pythagorean theorem: r^2 = x^2 + y^2 r^2 = (-5)^2 + (12)^2 r^2 = 25 + 144 r^2 = 169 r = sqrt(169) r = 13 Step 2: Sketch the diagram (3.1). • Draw a Cartesian plane with the x-axis and y-axis. • Mark the origin (0,0). • Plot the point P(-5, 12) in the second quadrant. • Draw a line segment from the origin to P(-5, 12). This represents the hypotenuse r=13. • Drop a perpendicular line from P(-5, 12) to the x-axis, meeting it at (-5, 0). This forms a right-angled triangle. • Label the horizontal side as x=-5, the vertical side as y=12, and the hypotenuse as r=13. • Indicate the angle measured counter-clockwise from the positive x-axis to the line segment OP. • Indicate the reference angle _R inside the triangle, between the line segment OP and the negative x-axis. Step 3: Determine + (3.2.1). Using the values from Step 1: = (y)/(r) = (12)/(13) = (x)/(r) = (-5)/(13) Now, calculate the sum: + = (12)/(13) + (-5)/(13) + = (12 - 5)/(13) + = (7)/(13) Step 4: Determine the value of (3.2.2). First, find the reference angle _R using the absolute value of : _R = | (12)/(-5) | = (12)/(5) Since the problem states "without the use of calculator", we express _R using : _R = ((12)/(5)) As is in the second quadrant (90^ 180^), the relationship between and _R is: = 180^ - _R Substitute the expression for _R: = 180^ - ((12)/(5)) Send me the next one 📸