Answer:
x = 65.26 degrees or x = 245.26 degrees.
Explanation:
To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:
4tan(x) = 7
Then, we can divide both sides by 4 to get:
tan(x) = 7/4
Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:
x = tan^-1(7/4)
Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).
However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).
To find the solution in the first quadrant, we can simply use the value we just calculated:
x = 65.26 degrees (rounded to two decimal places)
To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:
x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)
So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:
x = 65.26 degrees or x = 245.26 degrees.