Solve for θ to 2 decimal places if 0 360θ° ≤ < ° .a) cos 0 6667
Question
Solve for θ to 2 decimal places if 0 360θ° ≤ < ° .a) cos 0 6667
Solution
To solve for θ when cos θ = 0.6667 within the range of 0° ≤ θ < 360°, follow these steps:
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Use the inverse cosine function (also known as arccos) to find the principal value (the value within the range of 0° to 180°).
θ = arccos(0.6667)
If you use a calculator, make sure it's set to degrees. The result is approximately 48.19°.
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Since the cosine function is positive in both the first and fourth quadrants, there will be two solutions within the given range. The solution in the fourth quadrant will be 360° - θ.
So, the second solution is 360° - 48.19° = 311.81°.
Therefore, the solutions for θ to two decimal places are 48.19° and 311.81°.
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