Solve cos(x) = -0.44 on 0 (less than or equal to) x (less than) 2pi

There are two solutions, A and B, with A < B

Give your answers accurate to 3 decimal places

Why did the cosine go to the party alone? Because it couldn't find a sine to go with! Now let's find those solutions together, shall we?

To solve cos(x) = -0.44, we need to find the values of x that make the cosine of x equal to -0.44. Let's use a little trigonometric magic to find those solutions!

Step 1: Use the inverse cosine function (also known as arccos or cos^-1) to isolate x.
arccos(cos(x)) = arccos(-0.44)
x = arccos(-0.44)

Step 2: Calculate the value of arccos(-0.44) using a calculator.
x ≈ 1.136 radians (A solution)

Step 3: Since we need a second solution, let's add 2π to our first solution.
x ≈ 1.136 + 2π ≈ 7.955 radians (B solution)

Therefore, the solutions A and B, accurate to 3 decimal places, for cos(x) = -0.44 on the interval 0 ≤ x < 2π are:
A ≈ 1.136 radians
B ≈ 7.955 radians

Remember, A always comes before B because the alphabet says so. Keep having fun with math and trigonometry!

To solve the equation cos(x) = -0.44 on the interval 0 ≤ x < 2π, we can use the inverse cosine function or the unit circle.

First, let's use the inverse cosine function to find the principal solution:
cos^(-1)(-0.44) = approximately 1.125 radians

This gives us one solution, A = 1.125.

To find the second solution, we can use the fact that cosine has a periodicity of 2π. By adding 2π to the principal solution, we can find another solution:
A + 2π = 1.125 + 2π = approximately 7.407 radians

This gives us the second solution, B = 7.407.

Therefore, the two solutions to cos(x) = -0.44 on the interval 0 ≤ x < 2π, with A < B, are:
A ≈ 1.125 radians
B ≈ 7.407 radians

To solve the equation cos(x) = -0.44 on the interval 0 ≤ x < 2π, we can start by taking the inverse cosine (also known as the arccosine) of both sides of the equation. This will allow us to isolate the variable x.

So, we have:

x = arccos(-0.44)

To find the arccosine of -0.44, we can use a calculator or a mathematical software that has the capability to calculate inverse trigonometric functions. When you input -0.44 into the arccosine function, it will give you the value of x in radians.

Using a calculator, we can find:

x ≈ 2.094

However, this single value of x is just one of the solutions. We are looking for two solutions: A and B, where A < B.

Since cosine is an even function, the cosine of an angle and its supplementary angle are equal in magnitude but opposite in sign. In other words: cos(A) = cos(π - A)

So, if we take the supplementary angle of 2.094 radians (π - 2.094), we will get the second solution.

π - 2.094 ≈ 1.048

Hence, we have two solutions on the interval 0 ≤ x < 2π:

Solution A: x ≈ 2.094 (accurate to 3 decimal places)
Solution B: x ≈ 1.048 (accurate to 3 decimal places)

Remember, A < B in this case.