All solutions in interval [0,2pi) of cosine theta plus one equals zero
lets set theta = x
cos x + 1 = 0
lets solve for x
cos x = -1
x = arccos -1 arccos is inverse of cos.
Now what values would make cos -1?
Answer: 180 degrees.
cos theta plus one equal to zero
To find the solutions to the equation cos(theta) + 1 = 0 in the interval [0, 2pi), we need to solve for theta.
The equation is cos(theta) + 1 = 0.
First, subtract 1 from both sides of the equation:
cos(theta) = -1
To find the values of theta, we recognize that -1 is the x-coordinate of the point on the unit circle that is 180 degrees away from the origin. This point occurs at the angle pi radians.
However, we are looking for solutions in the interval [0, 2pi), so we can add 2pi to the angle pi to find all the solutions.
theta = pi + 2pi * n
where n is an integer.
Therefore, the solutions to the equation cos(theta) + 1 = 0 in the interval [0, 2pi) are:
theta = pi, 3pi, 5pi, 7pi, ...
Note that these are the angles in radians. If you want the angles in degrees, you can use the conversion formula: degrees = radians * (180/pi).