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
Let's break down the solution for 2 = -1 for 180^ 360^. Step 1: Isolate . First, we want to get by itself on one side of the equation. 2 = -1 Divide both sides by 2: = -(1)/(2) Step 2: Find the reference angle. The reference angle () is the acute angle formed with the x-axis. To find it, we ignore the negative sign for a moment and consider = (1)/(2). = ((1)/(2)) We know that (60^) = (1)/(2), so: = 60^ Step 3: Determine the quadrants where is negative. The cosine function is negative in the second and third quadrants. • In the first quadrant, all trigonometric functions are positive. • In the second quadrant, only sine is positive (cosine is negative). • In the third quadrant, only tangent is positive (cosine is negative). • In the fourth quadrant, only cosine is positive. Step 4: Apply the given range 180^ 360^. We are looking for solutions for between 180^ and 360^. This range covers the third and fourth quadrants. Since must be negative (from Step 1), and our range includes the third and fourth quadrants, we must look for the angle in the third quadrant because cosine is negative there. (In the fourth quadrant, cosine is positive). Step 5: Calculate the angle in the third quadrant. To find an angle in the third quadrant using the reference angle , we use the formula: = 180^ + Substitute the reference angle = 60^: = 180^ + 60^ = 240^ This angle 240^ is within the specified range of 180^ 360^. Therefore, the solution is: = 240^ That's 2 down. 3 left today — send the next one.