Answer to Question #190728 in Algebra for OhMoe

Question #190728

If arctan(tanα) = -2π/7 Which of the following values can have α have?

a) -9π/7

b) 2π/7

c) -5π/7

d) 5π/7


1
Expert's answer
2021-05-14T10:10:35-0400

Answer:-

arctan(x) is same as tan-1(x)




Graph of tan-1("x" )


We have given "tan^{-1}tan(\\alpha)=\\frac{-2\\pi}{7}"

According to question , we can have values of "\\alpha" as follows

(1) "y=\\alpha"

(2)"y=\\alpha-\\pi"

(3)"y=\\alpha+\\pi"


We got

"\\alpha=\\frac{-2\\pi}{7} from (1)"

"\\alpha=\\frac{-9\\pi}{7} \\ from(2)"

"\\alpha=\\frac{5\\pi}{7} \\ from (3)"

So , in the given question options (a) and (d) are possible.




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