Solve 9 tan x +5 =0, where 0 <= x <= 360

9 tan x +5 =0

tanx = -5/9
angle in standard position = 29.1°
(I took tan^-1 (5/9) )

so x = 180-29.1 or 360-29.1 , by CAST rule
x = 150.9° or 330.9°

To solve the equation 9 tan(x) + 5 = 0, where 0 <= x <= 360, we will first isolate the term containing the tangent function, and then solve for x by taking the inverse tangent.

1. Start by isolating the term with the tangent function:
Subtract 5 from both sides of the equation:
9 tan(x) = -5

2. Divide both sides of the equation by 9:
tan(x) = -5/9

3. To find the value of x, we will take the inverse tangent (also known as arctan or atan) of both sides. Using a calculator or a table, find the inverse tangent of -5/9, which is approximately -29.74 degrees.

4. Since the range given is 0 <= x <= 360, we need to find all solutions within this range.

-29.74 degrees is in the fourth quadrant, so we can add 180 degrees to find an equivalent angle in the first quadrant:
-29.74 + 180 = 150.26 degrees

Therefore, one solution is x = 150.26 degrees.

5. Additionally, since tangent has a period of 180 degrees, we can add another 180 degrees to find another solution in the fourth quadrant:
-29.74 + 180 + 180 = 330.26 degrees

Therefore, another solution is x = 330.26 degrees.

Hence, the solutions to the equation 9 tan(x) + 5 = 0, where 0 <= x <= 360, are x = 150.26 degrees and x = 330.26 degrees.