find the values of thiter between 0 degrees and 180 degrees such that 2cos thiter= 3sin thiter

Answer 1

To find the values of θ between 0 degrees and 180 degrees such that 2cosθ = 3sinθ, we can rearrange the equation:

2cosθ = 3sinθ
cosθ = (3/2)sinθ

We know that cosθ/sinθ is equal to cotθ, so we can rewrite the equation as:

cotθ = (3/2)

Now, we can determine the values of θ by taking the inverse cotangent of (3/2):

θ = arccot(3/2)

Using a calculator, we find that arccot(3/2) is approximately 33.69 degrees.

Therefore, the values of θ between 0 degrees and 180 degrees such that 2cosθ = 3sinθ are approximately 33.69 degrees.