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Select one or more expressions that together represent all solutions to the equation. Your answer should be in degrees.

7cos(9x)−1=1

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Answer:

To solve the equation 7cos(9x)−1=1, we first need to move the 1 to the left side of the equation:

7cos(9x) = 2

To find the solutions of the equation, we can divide both sides by 7:

cos(9x) = 2/7

Now we will use the inverse cosine function, denoted as arccos, to find the angle that has a cosine value of 2/7. Since the function cos is periodic with period 2Pi, it's range is [-1,1], we will look for the solutions between 0 and 2Pi.

x = (1/9)arccos(2/7) + (2kPi)/9 for k =0,1,2,....

we can also express the solution in degrees by multiplying the radian measure with 180/Pi.

x = (20/63)arccos(2/7) + (160*k) for k =0,1,2,....

or

x = (20/63) * arccos(2/7) * (180/pi) + (160*k) for k =0,1,2,....

where k is an integer.

So, x = (20/63) * arccos(2/7) * (180/pi) + (160*k) where k =0,1,2,.... is an expression that represents all solutions to the equation in degrees.

User Yousef Salimpour
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