Solve for θ in the equation cos θ = -0.181 when 180º < θ < 360º. Round your answer to the nearest tenth of a degree.
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To solve for θ in the equation cos θ = -0.181 when 180º < θ < 360º, we will need to use the inverse cosine function (also known as arccosine or cos⁻¹).
1. Begin by taking the inverse cosine of both sides of the equation:
θ = cos⁻¹(-0.181)
2. Using a calculator, find the inverse cosine of -0.181. Most scientific calculators have a cos⁻¹ function, usually denoted as "cos⁻¹" or "arccos." If you don't have a calculator on hand, you can use online calculators or software that perform trigonometric calculations.
3. Enter -0.181 into the inverse cosine function of your calculator or online tool, and compute the result. The output should be an angle.
4. Round the result to the nearest tenth of a degree, as instructed in the question, to find the value of θ.
Note: When taking the inverse cosine function, there are typically multiple possible angles that satisfy the equation. The given range of 180º < θ < 360º indicates that we want to find the angle in the third or fourth quadrant. But since the calculator only gives the principal value of the angle, we will need to adjust the result based on the given range.
For example, if the calculator gives the principal value of θ as 172.3º, we can adjust it to the angle in the correct range by adding 180º:
θ = 172.3º + 180º = 352.3º.
Therefore, the solution for θ, rounded to the nearest tenth of a degree, is 352.3º.