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blake1
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cos 6x=(1/2)
blake said:cos 6x=(1/2)
The principal value of cos 6x when it is equal to 1/2 is approximately 60 degrees or π/3 radians.
To solve cos 6x=(1/2) for principal values in degrees, you can use the inverse cosine function or the unit circle. Simply take the inverse cosine of 1/2, which is 60 degrees, and then divide by 6 to get the principal value of x as 10 degrees.
Yes, there are multiple principal values for cos 6x=(1/2) in degrees. This is because the cosine function is periodic and has a repeating pattern. The other possible principal values are 180 degrees or π radians plus the initial principal value of 10 degrees, resulting in 190 degrees or 7π/6 radians, and 360 degrees or 2π radians plus the initial principal value of 10 degrees, resulting in 370 degrees or 13π/6 radians.
Yes, you can solve cos 6x=(1/2) for principal values in radians using the same method as solving for degrees. The only difference is, you will use radians instead of degrees in your calculations.
The general solution for cos 6x=(1/2) in degrees is x = 10 + 360n, where n is any integer. This is because the cosine function repeats every 360 degrees, so adding or subtracting a multiple of 360 will result in another solution.