Find the exact value of cosx/2 given that cosx = 24/25.
Is this 49/50?
No, you have found cos^2 (x/2)
check your half-angle formulas.
Oops...forgot about the sqrt part in my calculations.
Is it 7/sqrt50?
To find the exact value of cos(x/2), given that cos(x) is 24/25, we can use the half-angle identity for cosine. The half-angle identity states that:
cos(x/2) = ±√((1 + cos(x))/2)
Since cos(x) is positive (since it is given as 24/25 which is positive) and the square root of a positive number is also positive, we can take the positive sign in front of the square root. Thus, we have:
cos(x/2) = √((1 + cos(x))/2)
Now, substitute the value of cos(x) into the formula:
cos(x/2) = √((1 + 24/25)/2)
= √((49/25)/2)
= √(49/50)
= 7/√50
To rationalize the denominator, we multiply the numerator and denominator by √50:
cos(x/2) = (7/√50) * (√50/√50)
= 7√50 / 50
Therefore, the exact value of cos(x/2), given that cos(x) is 24/25, is 7√50 / 50.
No, it is not equal to 49/50.