Question

How do you evaluate using a calculator of \[{\tan ^{ - 1}}( - 1.7321)\]?

Answer 1

Hint: The use of the basic trigonometric principle of ASTC and see how the values are changing their sign, and then select the desired time interval. You can also check the schedule, that of the tangent line of the function, to determine the positive and negative values.

Complete step by step answer:
The question is asking "What angle(s) has a \[\tan \] value of \[ - 1.7321\]
Firstly: In which quadrants is \[\tan \] negative?
Positive in \[1st\]and \[3rd\] and negative in \[2nd\] and \[4th\]
Then, find the root angle. Find \[{\tan ^{ - 1}}( + 1.7321)\]
This gives the acute angle in the \[1st\] quadrant from which we can get the angles in the other quadrants.
\[\theta = {\tan ^{ - 1}}(1.7321) = {60^ \circ }\]
We know that $1.732 = \sqrt 3 $
So, $\tan \sqrt 3 = 60^\circ $
After then, find the angles in the \[2nd\]and \[4th\]quadrants:
\[2nd\] quadrant:
\[{180^ \circ } - \theta = {180^ \circ } - {60^ \circ } = {120^ \circ }\]
4th quadrant:
\[{360^ \circ } - \theta = {360^ \circ } - {60^ \circ } = {300^ \circ }\]
Now check using a calculator to verify that:
\[\tan ({120^ \circ }) = - 1.7321\] and \[\tan ({300^ \circ }) = - 1.7321\]
These are the angles for \[0 \leqslant \theta \leqslant {360^ \circ }\]

Additional Information:
In mathematics, the trigonometric functions also called circular functions, angle functions or goniometric functions are real functions that relate to the angle of a right-angled triangle in terms of two side lengths. They are widely used in all sciences, and with respect to geometry, celestial mechanics, Instagram, and many, many more. The most widely used trigonometric functions are modern mathematics, the sine, cosine, and tangent. The links between them are respectively the cosecant, secant, and cot and each of the six trigonometric functions has a corresponding inverse function is the inverse of the trigonometric function. The tangent function is the most important trigonometric functions.

Note:
It is important to know the basic principles of trigonometry symbols, with the help of ASTC, and she knew where the change of signs in the input at different points in time. It is also important to know the features to achieve their maximum and minimum values.