solve for x, to the nearest degree, in the interval 0degres less than andequal to x greater than and equal to 360degrees.
cos^2x=1
4cos^2x=1
I will do the second one
4cos^2x=1
cos^2x = 1/4
cos x = ± 1/2
so x is in all 4 quadrants
we know cos 60º is 1/2
so x = 60º, 120º, 240º, 300º
the first one is even easier.
To solve for x in the equation cos^2x = 1, we can use the fact that the cosine function has a period of 360 degrees (or 2π radians). This means that the values of cos(x) repeat every 360 degrees.
Starting with the equation cos^2x = 1, we can take the square root of both sides to get:
cos x = ±1
Since the cosine function has a range of -1 to 1, we know that cos x can only be equal to 1 or -1.
Case 1: cos x = 1
In this case, x can be any angle where the cosine function is equal to 1. One such angle is 0 degrees, which is inside the given interval 0 degrees ≤ x ≤ 360 degrees.
Case 2: cos x = -1
In this case, x can be any angle where the cosine function is equal to -1. One such angle is 180 degrees, which is also within the given interval 0 degrees ≤ x ≤ 360 degrees.
Therefore, the solutions to the equation cos^2x = 1 in the interval 0 degrees ≤ x ≤ 360 degrees are x = 0 degrees and x = 180 degrees.