4 cos² x - 3 = 0
4 cos² x = 3
cos² x = 3/4
cos x = ±(√3)/2
Fixing the squared cosine doesn't discriminate among quadrants. There's one in every quadrant
cos x = ± cos(π/6)
Let's do plus first. In general, cos x = cos a has solutions x = ±a + 2πk integer k
cos x = cos(π/6)
x = ±π/6 + 2πk
Minus next.
cos x = -cos(π/6)
cos x = cos(π - π/6)
cos x = cos(5π/6)
x = ±5π/6 + 2πk
We'll write all our solutions as
x = { -5π/6, -π/6, π/6, 5π/6 } + 2πk integer k
42 ÷ 63
63 -> 420
63x6=378
420-378=42
63->420
So, how many times does 63 go into 42? Well, it doesn't. So put down a zero on your paper, and then a decimal. So if we add a zero onto 42, it becomes 420. Well, 420 is divisible by 63. In fact, 63 goes into 420 6 times, making a total of 378. 420-378 = 42. Then the process begins again. So you've got a 0.6, and that six just keeps on repeating. On paper, you're gonna wanna put a dash over the six to show that it's repeating.
Anyways, the answer is .66 repeating.
