Solve for ¥è in the equation tan ¥è = 2.42 when 180¨¬ < ¥è < 360¨¬. Round your answer to the nearest tenth of a degree. (Enter only the number.)
Come on, we just went through this at 3:36. This is the exact same kind of problem.
Find the quadrants where tan is positive, find the Arctan, and select the proper angle.
Is it 247.5484535°?
To solve for ¥è in the equation tan ¥è = 2.42, we can use the inverse tangent function, also known as the arctan function. The inverse tangent function will allow us to find the angle ¥è when we know the value of the tangent.
Here are the steps to solve for ¥è:
1. Use the arctan function on both sides of the equation: arctan(tan ¥è) = arctan(2.42).
2. Since the tangent function is periodic, meaning it repeats, we need to consider the given range of angles between 180¨¬ and 360¨¬ (exclusive).
3. In the given range, the arctan function will return an angle between -90¨¬ and 0¨¬ (exclusive). So, we need to find an angle in this range whose tangent is 2.42.
4. Use a scientific calculator or an online trigonometric calculator with an arctan function to find the angle whose tangent is 2.42.
arctan(2.42) = 65.41¨¬
5. Since the angle is in the range between 180¨¬ and 360¨¬, we need to add 180¨¬ to the result we obtained in the previous step.
65.41¨¬ + 180¨¬ = 245.41¨¬
Rounding the final answer to the nearest tenth of a degree, ¥è ≈ 245.4.