what is the smallest positive angle which satisfies the equation
2cosx-5cosx+2=0
-3 cos x = -2 ????
cos x = 2/3
x = inverse cos (.6666667) = 48.2 degrees
To find the smallest positive angle that satisfies the given equation, we need to solve the equation for x.
Let's rearrange the equation and combine like terms:
2cos(x) - 5cos(x) + 2 = 0
We can simplify this equation by combining the two cosine terms:
-3cos(x) + 2 = 0
Now, let's isolate the cosine term by moving the constant term to the other side of the equation:
-3cos(x) = -2
To solve for cos(x), divide both sides of the equation by -3:
cos(x) = -2 / -3
Since the range of cosine function is -1 to 1, we can conclude that -2 / -3 is within the range of the cosine function.
To find the angle x, we need to take the inverse cosine (or arccos) of -2 / -3. This will give us the angle whose cosine value is -2 / -3.
Using a calculator or mathematical software, we can find the inverse cosine of -2 / -3 to be approximately 0.8411 radians or 48.19 degrees.
Therefore, the smallest positive angle that satisfies the given equation is 0.8411 radians (or approximately 48.19 degrees).