To find the angle in radians for the value of the inverse tangent of negative 0.09 using a calculator: enter the inverse tangent function, use the +/- key for the negative sign, and input 0.09. There is definitely an angle in radians for tan¹ (-0.09), it is not the case that no angle exists.
Step-by-step explanation:
To find the angle in radians for the given value of the inverse tangent function, the steps on a calculator might look like this:
Use the Shift or second function to key in the tan¹ or arctan function.
Use the +/- key (or a separate button on some calculators) to input the negative sign before entering the numerical value 0.09.
After entering tan¹(-0.09) into the calculator, it should provide an answer in radians.
The inverse tangent function can take any real number value as input and will return an angle in radians between π/2 and -π/2, which includes negative values. So there will indeed be a corresponding angle in radians for tan¹ (-0.09), and it is not correct to say 'no such angle exists'.