Question

Use a calculator to solve the following equation for θ on the interval (0∘,180∘). cot(θ)=3.62 Round to one decimal place.

Answer 1

To solve the given equation cot(θ) = 3.62 on the interval (0∘,180∘), use the arctangent function to find the angle θ that satisfies the equation. The solution is approximately 74.6∘.

Step-by-step explanation:

To solve the equation cot(θ) = 3.62 on the interval (0∘,180∘), you can use a calculator to find the angle θ that satisfies the equation. Here are the steps:

1. Take the arctangent of both sides: arctan(cot(θ)) = arctan(3.62).
2. Since arctan(cot(θ)) simplifies to θ, we have θ = arctan(3.62).
3. Use a calculator to find the arctangent of 3.62. The result is approximately 74.6∘.
4. However, since the given interval is (0∘,180∘), we need to check if the angle 74.6∘ is within this interval. It is, so the solution is θ ≈ 74.6∘.