# Solve cos(x)=1/3, within the domain 0∘≤ x<360∘. ?

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- TomVLv 71 month ago
Since the cosine is positive, you know the answers are in the first and fourth quadrants. Use a calculator to find arccos(1/3). That will be the first quadrant solution. The fourth quadrant solution will be 360 - arccos(1/3).

cos(x) = 1/3

x = arccos(1/3), 360 - arccos(1/3)

x = 70.5°, 289.5° (to 1 decimal place)

Note: Calculators implement the arccosine function to return the angle for positive cosines in Q1 and for negative cosines in Q2. In other words, the range of the arccos(x) function is [0, π]. For solutions in Q3 and Q4, you must subtract the value returned by arccos(x) from 360° or 2π radians as appropriate.

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