(sinx)^(1/2)=cosx
x is between 0 and 90
What is sinx
sinx = cos^2x
sinx = 1-sin^2x
sin^2x + sinx - 1 = 0
now solve for sinx, and pick the positive solution.
Hey, one of my favourite numbers.
sinx = .618033989..
which is the decimal part of the Golden Ratio !
Neat!
the nice thing about Ø is that
Ø-1 = 1/Ø
To find the value of sin(x), we can use the given equation:
(sinx)^(1/2) = cos(x)
We know that cos(x) and sin(x) are related by the Pythagorean identity:
sin^2(x) + cos^2(x) = 1
Rearranging the given equation, we have:
sin(x) = cos^2(x)
Now let's use the value of x within the given range (between 0 and 90 degrees) to find the value of sin(x).
Since sin^2(x) + cos^2(x) = 1, we can substitute sin(x) with cos^2(x):
cos^2(x) + cos^2(x) = 1
Combining like terms, we get:
2cos^2(x) = 1
Dividing by 2, we have:
cos^2(x) = 1/2
Taking the square root of both sides, we get:
cos(x) = ±√(1/2)
Now, since x is between 0 and 90 degrees, we only need to consider the positive square root:
cos(x) = √(1/2)
Using the inverse cosine function (cos^(-1)), we can find the value of x:
x = cos^(-1)(√(1/2))
Evaluating this on a calculator or using a trigonometric table, we find:
x ≈ 45 degrees
Therefore, sin(x) is approximately equal to sin(45 degrees), which is:
sin(x) ≈ sin(45 degrees) ≈ 0.707