If 1-cos^2x=0.8725, and x is acute, determine the value of x correct to the nearest tenth of a degree.
Can someone please help me I am really strugling with this question. Thanks!
To determine the value of x, we first need to simplify the equation 1 - cos^2(x) = 0.8725. Let's rewrite cos^2(x) as (cos(x))^2:
1 - (cos(x))^2 = 0.8725
Now, let's solve for cos(x):
(cos(x))^2 = 1 - 0.8725
(cos(x))^2 = 0.1275
Taking the square root of both sides, we get:
cos(x) = √0.1275
Now, we need to find the value of x. Since x is acute, the cosine function is positive in the first and fourth quadrants. However, we can use the inverse cosine function (arccos) to find the value of x.
Using a calculator or a mathematical software, we can find the value of arccos(√0.1275) is approximately 1.411.
So, x is approximately arccos(√0.1275) = 1.411 radians.
To find the value of x in degrees, we multiply by 180/π (where π is approximately 3.14159):
x ≈ 1.411 * (180/π) ≈ 80.8 degrees
Therefore, the value of x, correct to the nearest tenth of a degree, is approximately 80.8 degrees.