Solve 1/2cot(x)>=1/2 over 0<=x<=2pi

Mathematics

1 answer:

RSB [31]2 years ago

3 0

9514 1404 393

Answer:

(0, π/4] ∪ (π, 5π/4]

Step-by-step explanation:

Multiplying by 2 gives ...

cot(x) ≥ 1

The cotangent function decreases from ∞ to 1 in the domain (0, π/4], and again in the domain (π, 5π/4]. The solution is the union of these two intervals.

x ∈ (0, π/4] ∪ (π, 5π/4]

_____

(a, b] is interval notation for a < x ≤ b

You might be interested in

Need help please, thanks!

MakcuM [25]

Given:
1 inch : 18 kilometers

Let us use the ratio and proportion method:

a:b = c:d where ad = bc

0.8 inches is 14.4 kilometers

1 : 18 = 0.8 : x
x = 0.8 * 18
x = 14.4 km

1.4 inches is 25.2 kilometers

1: 18 = 1.4 : x
x = 18 * 1.4
x = 25.2 km

2.1 inches is 37.8 kilometers

1 : 18 = 2.1 : x
x = 18 * 2.1
x = 37.8 km

4 0

2 years ago

Can the exponent in the denominator be subtracted from the exponent in the numerator when the based are different? Explain

Vanyuwa [196]

Answer:

No, Sorry.

Step-by-step explanation:

Since the bases are different, you'll have to change them even if they have a exponent or not. If you dunno how to make the denominators the same, just multiply the two by eachother.

Example) 1/2 - 3/4

$\frac{1}{2} - \frac{3}{4}$