Question

Solve the equation for 0° ≤ x ≤ 90°. Round to the nearest degree. 8cotθ + 3 = 5

Answer 1

θ = 76°

Step-by-step explanation:

The given equation is:

8 cotθ + 3 = 5

8 cotθ = 5-3

8 cotθ = 2

cot θ =
`(2)/(8) = (1)/(4)`

Now, we find θ

We know that the cot function is the inverse of the tan function.

The tan of an angle is positive in the first and third quadrants, therefore, the cot will be positive in the first and third quadrants as well

Now, we are given the condition:

0° ≤ x ≤ 90°

Therefore, we know for sure that our angle is in the first quadrant

θ = cot⁻¹(
`(1)/(4)`) = 75.96° = 76° to the nearest degree

Hope this helps :)