What is the smallest positive value of x that satisfies x= Arc cos 1/2
(x+5)=3
x=3-5
x=-2
x= Arc cos 1/2 <-----> cosx = 1/2
then x = π/3
check:
on your calculator, (set at degrees)
2ndF
cos
.5
=
to get 60° which is π/3 radians
yea
To find the smallest positive value of x that satisfies x = arccos(1/2), we need to look at the inverse cosine function and understand its behavior.
The arccosine function, denoted as arccos(x) or cos^(-1)(x), gives the angle whose cosine is x. In other words, it returns the value of an angle (in radians) whose cosine equals the given value.
In this case, we're looking for an angle whose cosine is 1/2.
From the unit circle, we know that the cosine function is positive in the first and fourth quadrants. Since we're looking for the smallest positive value of x, we focus on the first quadrant.
In the first quadrant, the cosine function is decreasing from 1 (at 0 degrees) to 0 (at 90 degrees). The cosine of 60 degrees is equal to 1/2. However, we need to convert this angle to radians, as the arccosine function takes radians as input.
To convert degrees to radians, we use the conversion factor of π/180. So, 60 degrees is equal to 60 * (π/180) radians, which simplifies to π/3.
Therefore, the smallest positive value of x that satisfies x = arccos(1/2) is x = π/3 (approximately equal to 1.047 radians).