In a right triangle, one angle measures x degrees where sin x degrees= 5/8. What is the value of cos (90 degrees-x) ?
"trick" question
the cosine of the complement equals the sine of the angle
To find the value of cos (90 degrees - x), let's first find the value of cos x.
Given that sin x = 5/8, we can use the Pythagorean identity to find the value of cos x.
Using the Pythagorean identity: sin^2 x + cos^2 x = 1
We know that sin x = 5/8, so we can substitute it into the equation:
(5/8)^2 + cos^2 x = 1
25/64 + cos^2 x = 1
cos^2 x = 1 - 25/64
cos^2 x = 39/64
Taking the square root of both sides:
cos x = ± √(39/64)
Since x is an angle in a right triangle, it lies in the first or second quadrant, so our solution will be positive:
cos x = √(39/64)
Now, let's find cos (90 degrees - x):
cos (90 degrees - x) is equal to sin x.
Therefore, cos (90 degrees - x) = sin x = 5/8.
To find the value of cos(90 degrees - x), we first need to find the value of x.
Given that sin(x) = 5/8, we can use the inverse sine function (also known as arcsine or sin^-1) to find the value of x.
sin(x) = 5/8
Using the inverse sine function, we can write this as:
x = sin^-1(5/8)
Now, using a calculator, we can find the value of x.
Let's assume that x is measured in degrees. So, we have:
x = sin^-1(5/8) ≈ 38.69 degrees
Since we know the value of x, we can now find the value of cos(90 degrees - x).
cos(90 degrees - x) = cos(90 - 38.69) = cos(51.31 degrees)
Using a calculator, we can find the value of cos(51.31 degrees).
cos(51.31 degrees) ≈ 0.622
Therefore, the value of cos(90 degrees - x) is approximately 0.622.