cos(t)=3/5 determine the exact value of t to the nearest degree
run do not walk to your calculator and figure
arccos(3/5) = 53 degrees
Cos^-1 (3/5)
= 53 degrees. (This is also close to one radian)
To determine the exact value of t, we will first use the inverse cosine function (also known as arccos or cos^-1) to find the principal value of t.
The inverse cosine function, denoted as cos^-1(x) or arccos(x), takes an input value x between -1 and 1 and returns the corresponding angle in radians between 0 and π (or 0 and 180°).
In this case, we have cos(t) = 3/5. So, we will find the principal value of t using the inverse cosine function:
t = cos^-1(3/5)
To find this value, you can use a scientific calculator that has the inverse cosine function (cos^-1) or an online calculator that provides inverse trigonometric functions.
Using a calculator or online tool, we find that cos^-1(3/5) is approximately 0.9273 radians.
To convert this value to degrees, we use the fact that π radians is equal to 180 degrees:
t (in degrees) = 0.9273 * (180/π)
t (in degrees) ≈ 53.13 degrees
So, the exact value of t to the nearest degree is approximately 53 degrees.