Find all angles, 0, degrees, is less than or equal to, A, is less than, 360, degrees0 ∘ ≤A<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).6, tangent, A, plus, 6, equals, 3, tangent, A, plus, 46tanA+6=3tanA+4

The given equation is 6tanA + 6 = 3tanA + 4.

First, let's simplify this equation by subtracting 3tanA from both sides:

6tanA - 3tanA = 4 - 6

This simplifies to:

3tanA = -2

Next, divide both sides by 3 to isolate tanA:

tanA = -2/3

Now, we need to find the angle A that satisfies this equation. We can do this by taking the arctangent (inverse tangent) of -2/3:

A = arctan(-2/3)

Using a calculator, we find that A is approximately -33.7 degrees. However, this is not within the range 0 ≤ A < 360 degrees.

To find an angle within this range, we can add 180 degrees to -33.7 degrees (since the period of the tangent function is 180 degrees):

A = -33.7 degrees + 180 degrees = 146.3 degrees

So, the angle A that satisfies the given equation within the range 0 ≤ A < 360 degrees is approximately 146.3 degrees.

However, since the period of the tangent function is 180 degrees, there is another solution within the given range. We can find this by adding 180 degrees to our first solution:

A = 146.3 degrees + 180 degrees = 326.3 degrees

So, the angles A that satisfy the given equation within the range 0 ≤ A < 360 degrees are approximately 146.3 degrees and 326.3 degrees.

The given equation is 6tanA + 6 = 3tanA + 4.

First, let's simplify this equation by subtracting 3tanA from both sides:

6tanA - 3tanA = 4 - 6

This simplifies to:

3tanA = -2

Next, divide both sides by 3 to solve for tanA:

tanA = -2/3

Now, we need to find the angle A that gives a tangent of -2/3. We can do this using the inverse tangent function (also known as arctan or tan^-1).

A = arctan(-2/3)

This will give us the principal value of A, which is the value of A in the interval from -90 degrees to 90 degrees. However, we want to find all values of A in the interval from 0 degrees to 360 degrees.

The tangent function has a period of 180 degrees, which means that if A is a solution, then A + 180n is also a solution for any integer n.

So, the solutions in the interval from 0 degrees to 360 degrees are:

A = arctan(-2/3) + 180n

We can use a calculator to find the value of arctan(-2/3), and then add 180n until we get a value in the desired interval.

Please note that the exact values will depend on the specific calculator used, and the answer should be rounded to the nearest tenth of a degree if necessary.