Solve the equation: \(\displaystyle{\tan{{\left({2}{x}+{1.426}\right)}}}=-{2.156}\)

ropowiec2gkc

ropowiec2gkc

Answered question

2022-03-20

Solve the equation:
tan(2x+1.426)=2.156

Answer & Explanation

horieblersee275

horieblersee275

Beginner2022-03-21Added 17 answers

The tangent function is periodic with period π. Thus, tanx=tan(x+nπ) for all integer values of n.
Here, tan(2x+1.426)=2.156 implies that tan(2x+1.426+nπ)=2.156. Thus, we have
tan(2x+1.426+nπ)=2.156
(2x+1.426+nπ)=arctan(2.156)
x=12(arctan(2.156)+1.426+nπ)
1.2812538747+mπ2
where m=n. Inasmuch as n can be any integer, negative or positive m can also be any integer.

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