I asked this question yesterday, but I am still having alot of trouble, can someone please help me. Thanks.

If 1-cos^2x=0.8725, and x is acute, determine the value of x correct to the nearest tenth of a degree.

1-cos^2x=0.8725

cos^2(x) = .1575
cosx = ± .35707

since x is acute, it must be in the first quadrant, so just take the inverse cosine of .35707 to get
x = 69.1º

Of course, I'd be happy to help you solve this problem. To find the value of x in the equation 1 - cos^2(x) = 0.8725, we will follow these steps:

Step 1: Rearrange the equation
The formula 1 - cos^2(x) is equivalent to sin^2(x). Therefore, we can rewrite the equation as sin^2(x) = 0.8725.

Step 2: Solve for sin(x)
To solve for sin(x), we take the square root of both sides of the equation: sin(x) = √0.8725.

Step 3: Solve for x
Now, to find the value of x, we need to use the inverse sine function (also known as arcsine or sin^(-1)). This will give us the angle (x) whose sine is equal to √0.8725.

Using a calculator or a mathematical software, find the arcsine (or sin^(-1)) of √0.8725. The result will be the value of x in radians.

Step 4: Convert radians to degrees
As the question asks for the value of x in degrees, we need to convert the calculated value from radians to degrees. To do this, multiply the value in radians by 180/π (approximately 57.296).

Round the result to the nearest tenth of a degree, and that will be your answer for x.

Please let me know if you need any further clarification or assistance with the steps.