Question 217224
Note: the answer will vary depending on what mode you are in (either degrees or radians).



What you're looking for is the value of *[Tex \LARGE \theta] that will satisfy *[Tex \LARGE \tan(\theta)=1.4739716]. To find *[Tex \LARGE \theta], you need to apply the arctangent to both sides. This will effectively 'undo' the tangent on the left side and cancel it out (which will isolate *[Tex \LARGE \theta]).



If you're not sure how to do what I described above, then read on...



*[Tex \LARGE \tan(\theta)=1.4739716] ... Start with the given equation.



*[Tex \LARGE \tan^{-1}\left(\tan(\theta)\right)=\tan^{-1}\left(1.4739716\right)] ... Take the arctangent of both sides.



*[Tex \LARGE \theta=\tan^{-1}\left(1.4739716\right)] ... Evaluate the arctangent of the tangent of *[Tex \LARGE \theta] to get *[Tex \LARGE \theta]



*[Tex \LARGE \theta=55.845+180n] ... Evaluate the arctangent of 1.4739716 to approximately get 55.845 degrees. Remember to add on multiples of 180 to account for all solutions.



Note: make sure you're in the right mode when you take the arctangent of  1.4739716


If you're supposed to be in radian mode, then...



*[Tex \LARGE \theta=0.975+\pi n] ... Evaluate the arctangent of 1.4739716 to approximately get 55.845 degrees. Remember to add on multiples of *[Tex \LARGE \pi] to account for all solutions.



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Answer:



Depending on the mode that you're supposed to use, the solutions are:



*[Tex \LARGE \theta=55.845+180n] (if you're working with degrees)



or...



*[Tex \LARGE \theta=0.975+\pi n] (if you're working with radians)